Solution: The frequency of a steam train whistle as it

A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.5 s after shouting. Estimate the length of the lake.

A sailor strikes the side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.0 s later. How deep is the ocean at this point? Assume the speed of sound in sea water is (Table 121) and does not vary significantly with depth.

(a) Calculate the wavelengths in air at 20C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b) What is the wavelength of an 18-MHz ultrasonic wave?

On a warm summer day (31C), it takes 4.80 s for an echo to return from a cliff across a lake. On a winter day, it takes 5.20 s. What is the temperature on the winter day?

An ocean fishing boat is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.55 km away (Fig. 1233). How much time elapses before the backfire is heard (a) by the fish, and (b) by the fishermen?

A person, with his ear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 0.80 s apart. How far away did the impact occur? See Table 121.

(III) A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 2.7 s later. How high is the cliff?

What is the intensity of a sound at the pain level of 120 dB? Compare it to that of a whisper at 20 dB

What is the sound level of a sound whose intensity is 1.5 * 106 Wm2?

You are trying to decide between two new stereo amplifiers. One is rated at 75 W per channel and the other is rated at 120 W per channel. In terms of dB, how much louder will the more powerful amplifier be when both are producing sound at their maximum levels?

If two firecrackers produce a combined sound level of 85 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dBs.]

A person standing a certain distance from an airplane with four equally noisy jet engines is experiencing a sound level of 140 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dBs.]

One CD player is said to have a signal-to-noise ratio of 82 dB, whereas for a second CD player it is 98 dB. What is the ratio of intensities of the signal and the background noise for each device?

A 55-dB sound wave strikes an eardrum whose area is (a) How much energy is received by the eardrum per second? (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J

At a rock concert, a dB meter registered 130 dB when placed 2.5 m in front of a loudspeaker on stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air? (b) How far away would the sound level be 85 dB?

A fireworks shell explodes 100 m above the ground, creating colorful sparks. How much greater is the sound level of the explosion for a person at a point directly below the explosion than for a person a horizontal distance of 200 m away (Fig. 1234)?

If the amplitude of a sound wave is made 3.5 times greater, (a) by what factor will the intensity increase? (b) By how many dB will the sound level increase?

Two sound waves have equal displacement amplitudes, but one has 2.2 times the frequency of the other. What is the ratio of their intensities?

What would be the sound level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 440 Hz?

(a) Estimate the power output of sound from a person speaking in normal conversation. Use Table 122. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. (b) How many people would it take to produce a total sound output of 60 W of ordinary conversation? [Hint: Add intensities, not dBs.]

Expensive amplifier A is rated at 220 W, while the more modest amplifier B is rated at 45 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp. (b) Will the expensive amp sound twice as loud as the cheaper one?

A 5000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 126.)

What are the lowest and highest frequencies that an ear can detect when the sound level is 40 dB? (See Fig. 126.)

Your ears can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at (a) 100 Hz, (b) 5000 Hz? (See Fig. 126.)

Estimate the number of octaves in the human audible range, 20 Hz to 20 kHz.

(I) What would you estimate for the length of a bass clarinet, assuming that it is modeled as a closed tube and that the lowest note that it can play is a D? whose frequency is 69 Hz ?

The A string on a violin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has mass 0.35 g. Under what tension must the string be placed?

An organ pipe is 116 cm long. Determine the fundamental and first three audible overtones if the pipe is (a) closed at one end, and (b) open at both ends.

(I) (a) What resonant frequency would you expect from blowing across the top of an empty soda bottle that is 24 cm deep, if you assumed it was a closed tube? (b) How would that change if it was one-third full of soda?

If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?

A tight guitar string has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 70% of its original length?

(II) Estimate the frequency of the “sound of the ocean” when you put your ear very near a 15-cm-diameter seashell (Fig. 12–35).

(II) An unfingered guitar string is 0.68 m long and is tuned to play E above middle C (330 Hz). (a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the wavelength on the string of this 440-Hz wave? (c) What are the frequency and wavelength of the sound wave produced in air at 22°C by this fingered string?

(II) (a) Determine the length of an open organ pipe that emits middle C262 Hz when the temperature is \(18^{\circ} \mathrm{C}\). (b) What are the wavelength and frequency of the fundamental standing wave in the tube? (c) What are \(\lambda\) and \(f\) in the traveling sound wave produced in the outside air? Equation Transcription: Text Transcription: 18^circ lambda f

(II) An organ is in tune at 22.0°C. By what percent will the frequency be off at 11°C?

(II) How far from the mouthpiece of the flute in Example 12–11 should the hole be that must be uncovered to play F above middle C at 349 Hz?

(II) (a) At \(T=22^{\circ} \mathrm{C}\), how long must an open organ pipe be to have a fundamental frequency of 294 Hz ? (b) If this pipe is filled with helium, what is its fundamental frequency? Equation Transcription: Text Transcription: T=22 ^circ C

(II) A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe?

A uniform narrow tube 1.70 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?

(II) A pipe in air at 23.0°C is to be designed to produce two successive harmonics at 280 Hz and 320 Hz. How long must the pipe be, and is it open or closed?

(II) How many overtones are present within the audible range for a 2.18-m-long organ pipe at \(20^{\circ}C\) (a) if it is open, and (b) if it is closed?

Determine the fundamental and first overtone frequencies when you are in a 9.0-m-long hallway with all doors closed. Model the hallway as a tube closed at both ends

When a players finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the strings fundamental frequency (see Fig. 1236). The strings tension and mass per unit length remain unchanged. If the unfingered length of the string is determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note compared to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 2112.

(III) The human ear canal is approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6?

(II) Approximately what are the intensities of the first two overtones of a violin compared to the fundamental? How many decibels softer than the fundamental are the first and second overtones? (See Fig. 12–15.)

A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one of which is sounding 350 Hz. How far off in frequency is the other string?

A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If humans can hear neither whistle when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.

(II) What is the beat frequency if middle C(262 Hz) and \(\mathrm{C}^{\#}\) (277 Hz) are played together? What if each is played two octaves lower (each frequency reduced by a factor of 4)? Equation Transcription: Text Transcription: C^#

(II) A guitar string produces 3 beats/s when sounded with a 350-Hz tuning fork and 8 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.

(II) Two violin strings are tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.5%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]

(II) The two sources of sound in Fig. 12-16 face each other and emit sounds of equal amplitude and equal frequency (305 Hz) but \(180^{\circ}\) out of phase. For what minimum separation of the two speakers will there be some point at which (a) complete constructive interference occurs and (b) complete destructive interference occurs. (Assume \(T=20^{\circ} \mathrm{C}\).) Equation Transcription: Text Transcription: 180^circ T=20^circ C

Two piano strings are supposed to be vibrating at 220 Hz, but a piano tuner hears three beats every 2.5 s when they are played together. (a) If one is vibrating at 220.0 Hz, what must be the frequency of the other (is there only one answer)? (b) By how much (in percent) must the tension be increased or decreased to bring them in tune?

(III) Two loudspeakers are 1.60 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. (a) What is the lowest frequency at which destructive interference will occur at this point if the speakers are in phase? (b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let \(T=20^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: T=20^circ C

(III) Two loudspeakers are placed 3.00 m apart, as shown in Fig. 12–37. They emit 474-Hz sounds, in phase. A microphone is placed 3.20 m distant from a point midway between the two speakers, where an intensity maximum is recorded. (a) How far must the microphone be moved to the right to find the first intensity minimum? (b) Suppose the speakers are reconnected so that the 474-Hz sounds they emit are exactly out of phase. At what positions are the intensity maximum and minimum now?

(III) A source emits sound of wavelengths 2.54 m and 2.72 m in air. (a) How many beats per second will be heard? (Assume \(T=20^\circ \mathrm C.\) ) (b) How far apart in space are the regions of maximum intensity?

(I) The predominant frequency of a certain fire truck’s siren is 1650 Hz when at rest. What frequency do you detect if you move with a speed of 30.0 m/s (a) toward the fire truck, and (b) away from it?

(II) A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 27.5 m/s. What is the received sound frequency?

(II) Two automobiles are equipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 18 m/s the driver at rest hears a beat frequency of 4.5 Hz. What is the frequency the horns emit? Assume \(T=20^{\circ} \mathrm{C}\). Equation Transcription: Text Transcription: T=20^circ C

(II) As a bat flies toward a wall at a speed of 6.0 m/s the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?

(II) In one of the original Doppler experiments, a tuba was played at a frequency of 75 Hz on a moving flat train car, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard in the station if the train car approached the station at a speed of 14.0 m/s?

(II) A wave on the ocean surface with wavelength 44 m travels east at a speed of relative to the ocean floor. If, on this stretch of ocean, a powerboat is moving at 14 m/s (relative to the ocean floor), how often does the boat encounter a wave crest, if the boat is traveling (a) west, and (b) east?

(III) A police car sounding a siren with a frequency of 1580 Hz is traveling at 120.0 km/h (a) What frequencies does an observer standing next to the road hear as the car approaches and as it recedes? (b) What frequencies are heard in a car traveling at 90.0 km/h in the opposite direction before and after passing the police car? (c) The police car passes a car traveling in the same direction at 80.0 km/h. What two frequencies are heard in this car?

(III) The Doppler effect using ultrasonic waves of frequency \(2.25 \times 10^6\ Hz\) is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 240 Hz is observed. Assuming that the speed of sound in tissue is 1540 m/s, calculate the maximum velocity of the surface of the beating heart.

(I) (a) How fast is an object moving on land if its speed at 24°C is Mach 0.33? (b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.1 on a screen. What is the speed of sound at that altitude?

(I) The wake of a speedboat is 12° in a lake where the speed of the water wave is 2.2 km/h. What is the speed of the boat?

(II) An airplane travels at Mach 2.1 where the speed of sound is 310 m/s. (a) What is the angle the shock wave makes with the direction of the airplane’s motion? (b) If the plane is flying at a height of 6500 m, how long after it is directly overhead will a person on the ground hear the shock wave?

(II) A space probe enters the thin atmosphere of a planet where the speed of sound is only about 42 m/s. (a) What is the probe’s Mach number if its initial speed is 15,000 km/h? (b) What is the angle of the shock wave relative to the direction of motion?

(II) A meteorite traveling 9200 m/s strikes the ocean. Determine the shock wave angle it produces (a) in the air just before entering the ocean, and (b) in the water just after entering. Assume \(T=20^{\circ} \mathrm{C}\) . Equation Transcription: Text Transcription: T=20^circ C

(III) You look directly overhead and see a plane exactly 1.45 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12-38. Determine (a) the angle of the shock cone, \(\theta\), and (b) the speed of the plane and its Mach number. Assume the speed of sound is 330 m/s. Equation Transcription: Text Transcription: theta

(III) A supersonic jet traveling at Mach 2.0 at an altitude of 9500 m passes directly over an observer on the ground. Where will the plane be relative to the observer when the latter hears the sonic boom? (See Fig. 12–39.)

A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 85 m, what is the minimum time between pulses (in fresh water)?

A single mosquito 5.0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 200 such mosquitoes?

What is the resultant sound level when an 81-dB sound and an 87-dB sound are heard simultaneously?

The sound level 8.25 m from a loudspeaker, placed in the open, is 115 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?

A stereo amplifier is rated at 225 W output at 1000 Hz. The power output drops by 12 dB at 15 kHz. What is the power output in watts at 15 kHz?

Workers around jet aircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 130 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?

In audio and communications systems, the gain, \(\beta\), in decibels is defined for an amplifier as \(\beta=10 \log \left(\frac{P_{\text {out }}}{P_{\text {in }}}\right)\) where \(P_{\text {in }}\) is the power input to the system and \(P_{\text {out }}\) is the power output. (a) A particular amplifier puts out \(135 \mathrm{~W}\) of power for an input of \(1.0 \mathrm{~mW}\). What is its gain in dB ? (b) If a signal-to-noise ratio of 93 dB is specified, what is the noise power if the output signal is \(10 \mathrm{~W}\) ? Equation Transcription: Text Transcription: beta beta=10 log (P_out/P_in) P_in P_out 135 W 1.0 m W 10 W

Manufacturers typically offer a particular guitar string in a choice of diameters so that players can tune their instruments with a preferred string tension. For example, a nylon high-E string is available in a low- and high-tension model with diameter 0.699 mm and 0.724 mm, respectively. Assuming the density \(\rho\) of nylon is the same for each model, compare (as a ratio) the tension in a tuned high- and low-tension string.

A tuning fork is set into vibration above a vertical open tube filled with water (Fig. 12–40). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?

Two identical tubes, each closed at one end, have a fundamental frequency of 349 Hz at 25.0°C. The air temperature is increased to 31.0°C in one tube. If the two pipes are now sounded together, what beat frequency results?

Each string on a violin is tuned to a frequency \(1 \frac{1}{2}\) times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string? Equation Transcription: Text Transcription: 1 1/2

A particular whistle produces sound by setting up the fundamental standing wave in an air column 7.10 cm long. The tube is closed at one end. The whistle blower is riding in a car moving away from you at 25 m/s. What frequency do you hear?

The diameter D of a tube does affect the node at the open end of a tube. The end correction can be roughly approximated as adding D/3 to \(\ell\) to give us an effective length for the tube in calculations. For a closed tube of length 0.55 m and diameter 3.0 cm, what are the frequencies of the first four harmonics, taking the end correction into consideration?

The frequency of a steam train whistle as it approaches you is 565 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?

Two trains emit 508-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.5-Hz beat frequency when the other train approaches. What is the speed of the moving train?

Two loudspeakers are at opposite ends of a railroad car as it moves past a stationary observer at 12.0 m/s as shown in Fig. 12–41. If the speakers have identical sound frequencies of 348 Hz, what is the beat frequency heard by the observer when (a) he listens from position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

Two open organ pipes, sounding together, produce a beat frequency of 6.0 Hz. The shorter one is 2.40 m long. How long is the other?

A bat flies toward a moth at speed 7.8 m/s while the moth is flying toward the bat at speed 5.0 m/s. The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?

A bat emits a series of high-frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one pulse returns before the next pulse is emitted?

Two loudspeakers face each other at opposite ends of a long corridor. They are connected to the same source which produces a pure tone of 282 Hz. A person walks from one speaker toward the other at a speed of 1.6 m/s. What “beat” frequency does the person hear?

A sound-insulating door reduces the sound level by 30 dB. What fraction of the sound intensity passes through this door?

The "alpenhorn" (Fig. 12-42) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the \(\mathrm{F}^{\#}\) (or G? ) horn. What is the fundamental frequency of this horn, and which overtone is close to \(\mathrm{F}^{\#}\)? (See Table 12-3.) Model as a tube open at both ends. Equation Transcription: G? Text Transcription: F^# G^b F^#

Room acoustics for stereo listening can be compromised by the presence of standing waves, which can cause acoustic dead spots at the locations of the pressure nodes. Consider a living room 4.7 m long, 3.6 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.

A dramatic demonstration, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For an 80-cm-long rod, (a) what is the fundamental frequency of the sound? (b) What is its wavelength in the rod, and (c) what is the traveling wavelength of the sound in air at 20°C?

The intensity at the threshold of hearing for the human ear at a frequency of about 1000 Hz is \(I_0 = 1.0 \times 10^{-12}\ W/m^2\), for which \(\beta\), the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or \(I = 1.0\ W/m^2\), corresponding to an increase of intensity by a factor of \(10^{12}\). By what factor does the displacement amplitude, A, vary?

A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is about 1540 m/s. What is the expected beat frequency if blood is flowing in large leg arteries at 3.0 cm/s directly away from the sound source?

Problem 1COQ A pianist plays the note “middle C.” The sound is made by the vibration of the piano string and is propagated outward as a vibration of the air (which can reach your ear). How does the vibration on the string compare to the vibration in the air? (a) The vibration on the string and the vibration in the air have the same wavelength. (b) They have the same frequency. (c) They have the same speed. (d) Neither wavelength, frequency, nor speed are the same in the air as on the string.

Do you expect an echo to return to you more quickly on a hot day or a cold day? (a) Hot day. (b) Cold day. (c) Same on both days.

Problem 1P (I) A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.5 s after shouting. Estimate the length of the lake.

What is the evidence that sound travels as a wave?

Problem 1SL At a painfully loud concert, a 120-dB sound wave travels away from a loudspeaker 343 m/s. at How much sound wave energy is contained in each 1.0 –cm3 volume of air in the region near this loudspeaker? (See Sections 12–2 and 11–9.)

Sound waves are (a) transverse waves characterized by the displacement of air molecules. (b) longitudinal waves characterized by the displacement of air molecules. (c) longitudinal waves characterized by pressure differences. (d) Both (b) and (c). (e) (a), (b), and (c).

Problem 2P (I) A sailor strikes the side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.0 s later. How deep is the ocean at this point? Assume the speed of sound in sea water is 1560 m/s (Table 12–1) and does not vary significantly with depth.

What is the evidence that sound is a form of energy?

At a race track, you can estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?

The sound level near a noisy air conditioner is 70 dB. If two such units operate side by side, the sound level near them would be (a) 70 dB. (b) 73 dB. (c) 105 dB. (d) 140 dB.

Problem 3P (I) (a) Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b) What is the wavelength of an 18-MHz ultrasonic wave?

Children sometimes play with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

Problem 3SL A person hears a pure tone in the 500 to 1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.25 m farther from one source than the other. What is the frequency of the sound?

Problem 4P (II) On a warm summer day (31°C), it takes 4.80 s for an echo to return from a cliff across a lake. On a winter day, it takes 5.20 s. What is the temperature on the winter day?

To make a given sound seem twice as loud, how should a musician change the intensity of the sound? (a) Double the intensity. (b) Halve the intensity. (c) Quadruple the intensity. (d) Quarter the intensity. (e) Increase the intensity by a factor of 10.

When a sound wave passes from air into water, do you expect the frequency or wavelength to change?

Problem 4SL A factory whistle emits sound of frequency 770 Hz. The wind velocity 15.0 m/s is from the north (heading south). What frequency will observers hear who are located, at rest, (a) due north, (b) due south, (c) due east, and (d) due west, of the whistle? What frequency is heard by a cyclist heading (e) north or (f) west, toward the whistle at 12.0 m/s? Assume T =20°C.

Problem 5MCQ A musical note that is two octaves higher than a second note (a) has twice the frequency of the second note. (b) has four times the frequency of the second note. (c) has twice the amplitude of the second note. (d) is 3 dB louder than the second note. (e) None of the above.

What evidence can you give that the speed of sound in air does not depend significantly on frequency?

Problem 5Q What evidence can you give that the speed of sound in air does not depend significantly on frequency?

Problem 5SL A bugle is a tube of fixed length that behaves as if it is open at both ends. A bugler, by adjusting his lips correctly and blowing with proper air pressure, can cause a harmonic (usually other than the fundamental) of the air column within the tube to sound loudly. Standard military tunes like Taps and Reveille require only four musical notes: G4 (392 Hz), C5 (523 Hz), E5 (659 Hz), and G5 (784 Hz). (a) For a certain length l a bugle will have a sequence of four consecutive harmonics whose frequencies very nearly equal those associated with the notes G4, C5, E5, and G5. Determine this l (b) Which harmonic is each of the (approximate) notes G4, C5, E5, and G5 for the bugle?

Problem 6MCQ In which of the following is the wavelength of the lowest vibration mode the same as the length of the string or tube? (a) A string. (b) An open tube. (c) A tube closed at one end. (d) All of the above. (e) None of the above.

Problem 6P (II) A person, with his ear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 0.80 s apart. How far away did the impact occur? See Table 12–1.

The voice of a person who has inhaled helium sounds very high-pitched. Why?

Problem 7MCQ When a sound wave passes from air into water, what properties of the wave will change? (a) Frequency. (b)Wavelength. (c) Wave speed. (d) Both frequency and wavelength. (e) Both wave speed and wavelength.

(III) A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 2.7 s later. How high is the cliff?

How will the air temperature in a room affect the pitch of organ pipes?

A guitar string vibrates at a frequency of 330 Hz with wavelength 1.40 m. The frequency and wavelength of this sound in air (20°C) as it reaches our ears is (a) same frequency, same wavelength. (b) higher frequency, same wavelength. (c) lower frequency, same wavelength. (d) same frequency, longer wavelength. (e) same frequency, shorter wavelength.

Problem 8P (I) What is the intensity of a sound at the pain level of 120 dB? Compare it to that of a whisper at 20 dB.

Explain how a tube might be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler.)

A guitar player shortens the length of a guitar’s vibrating string by pressing the string straight down onto a fret. The guitar then emits a higher-pitched note, because (a) the string’s tension has been dramatically increased. (b) the string can vibrate with a much larger amplitude. (c) the string vibrates at a higher frequency.

Problem 9P (I) What is the sound level of a sound whose intensity is 1.5 X 10-6 W/m2?

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge?

Problem 10MCQ An organ pipe with a fundamental frequency f is open at both ends. If one end is closed off, the fundamental frequency will (a) drop by half. (b) not change. (c) double.

Problem 10P (II) You are trying to decide between two new stereo amplifiers. One is rated at 75 W per channel and the other is rated at 120 W per channel. In terms of dB, how much louder will the more powerful amplifier be when both are producing sound at their maximum levels?

A noisy truck approaches you from behind a building. Initially you hear it but cannot see it.When it emerges and you do see it, its sound is suddenly “brighter”—you hear more of the high-frequency noise. Explain. [Hint: See Section 11–14 on diffraction.]

Two loudspeakers are about 10 m apart in the front of a large classroom. If either speaker plays a pure tone at a single frequency of 400 Hz, the loudness seems pretty even as you wander around the room, and gradually decreases in volume as you move farther from the speaker. If both speakers then play the same tone together, what do you hear as you wander around the room? (a) The pitch of the sound increases to 800 Hz, and the sound is louder but not twice as loud. It is louder closer to the speakers and gradually decreases as you move away from the speakers—except near the back wall, where a slight echo makes the sound louder. (b) The sound is louder but maintains the same relative spatial pattern of gradually decreasing volume as you move away from the speakers. (c) As you move around the room, some areas seem to be dead spots with very little sound, whereas other spots seem to be louder than with only one speaker. (d) The sound is twice as loud—so loud that you cannot hear any difference as you move around the room. (e) At points equidistant from both speakers, the sound is twice as loud. In the rest of the room, the sound is the same as if a single speaker were playing.

Problem 11P (II) If two firecrackers produce a combined sound level of 85 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dBs.]

Standing waves can be said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Explain.

Problem 12EA If an increase of 3 dB means “twice as intense,” what does an increase of 6 dB mean?

From Table 12–2, we see that ordinary conversation corresponds to a sound level of about 65 dB. If two people are talking at once, the sound level is (a) 65 dB, (b) 68 dB, (c) 75 dB, (d) 130 dB, (e) 62 dB.

How many octaves does the piano of Example 12–8 cover?

Return to the Chapter-Opening Question, page 328, and answer it again now. Try to explain why you may have answered differently the first time.

Suppose the police car of Example 12–15 is at rest and emits at 1600 Hz. What frequency would you hear if you were moving at 25.0 m/s (a) toward it, and (b) away from it?

You are driving at 75 km/h. Your sister follows in the car behind at 75 km/h. When you honk your horn, your sister hears a frequency (a) higher than the frequency you hear. (b) lower than the frequency you hear. (c) the same as the frequency you hear. (d) You cannot tell without knowing the horn’s frequency.

How fast would a source have to approach an observer at rest for the observed frequency to be one octave above the produced frequency (frequency doubled)? (a) \(\frac{1}{2} v_{snd}\), (b) \(v_{snd}\), (c) \(2v_{snd}\), (d) \(4v_{snd}\).

Problem 12P (II) A person standing a certain distance from an airplane with four equally noisy jet engines is experiencing a sound level of 140 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dBs.]

In Fig. 12–16, if the frequency of the speakers is lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together? Explain.

A guitar string is vibrating at its fundamental frequency f. Which of the following is not true? (a) Each small section of the guitar string oscillates up and down at a frequency f. (b) The wavelength of the standing wave on the guitar string is \(\lambda=v / f\), where v is the velocity of the wave on the string. (c) A sound wave created by this vibrating string propagates through the air with frequency (d) A sound wave created by this vibrating string propagates through the air with wavelength \(\lambda=v / f\) where v is the velocity of sound in air. (e) The wavelength of the standing wave on the guitar string is \(\lambda = \ell\) where is ? the length of the string. Equation Transcription: Text Transcription: lambda = v/f lambda = ell

Problem 13P (II) One CD player is said to have a signal-to-noise ratio of 82 dB, whereas for a second CD player it is 98 dB. What is the ratio of intensities of the signal and the background noise for each device?

Traditional methods of protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Problem 14P (II) A 55-dB sound wave strikes an eardrum whose area Is 5.0 X 10-5m2 (a) How much energy is received by the eardrum per second? (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.

Problem 15P (II) At a rock concert, a dB meter registered 130 dB when placed 2.5 m in front of a loudspeaker on stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air? (b) How far away would the sound level be 85 dB?

Problem 15Q Is there a Doppler shift if the source and observer move in the same direction, with the same velocity? Explain.

(II) A fireworks shell explodes 100 m above the ground, creating colorful sparks. How much greater is the sound level of the explosion for a person at a point directly below the explosion than for a person a horizontal distance of 200 m away (Fig. 12–34)?

Problem 16Q If a wind is blowing, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed?

Problem 17P (II) If the amplitude of a sound wave is made 3.5 times greater, (a) by what factor will the intensity increase? (b) By how many dB will the sound level increase?

Figure 12–32 shows various positions of a child on a swing moving toward a person on the ground who is blowing a whistle. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

Problem 18P (II) Two sound waves have equal displacement amplitudes, but one has 2.2 times the frequency of the other. What is the ratio of their intensities?

Problem 19P (II) What would be the sound level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 440 Hz?

Problem 20P (II) (a) Estimate the power output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. (b) How many people would it take to produce a total sound output of 60 W of ordinary conversation? [Hint: Add intensities, not dBs.]

Problem 21P (III) Expensive amplifier A is rated at 220W, while the more modest amplifier B is rated at 45W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp. (b) Will the expensive amp sound twice as loud as the cheaper one?

(I) A 5000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)

(I) What are the lowest and highest frequencies that an ear can detect when the sound level is 40 dB? (See Fig. 12–6.)

(II) Your ears can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at (a) 100 Hz, (b) 5000 Hz? (See Fig. 12–6.)

Problem 25P (I) Estimate the number of octaves in the human audible range, 20Hz to 20 kHz.

Problem 26P (I) What would you estimate for the length of a bass clarinet, assuming that it is modeled as a closed tube and that the lowest note that it can play is d a whose frequency is 69 Hz?

Problem 27P (I) The A string on a violin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has mass 0.35 g. Under what tension must the string be placed?

(I) An organ pipe is 116 cm long. Determine the fundamental and first three audible overtones if the pipe is (a) closed at one end, and (b) open at both ends.

(I) (a) What resonant frequency would you expect from blowing across the top of an empty soda bottle that is 24 cm deep, if you assumed it was a closed tube? (b) How would that change if it was one-third full of soda?

Problem 30P (I) If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?

(II) A tight guitar string has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 70% of its original length?

(II) Estimate the frequency of the “sound of the ocean” when you put your ear very near a 15-cm-diameter seashell (Fig. 12–35).

Problem 33P (II) An unfingered guitar string is 0.68 m long and is tuned to play E above middle C (330 Hz). (a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the wavelength on the string of this 440-Hz wave? (c)What are the frequency and wavelength of the sound wave produced in air at 22°C by this fingered string?

Problem 34P (II) (a) Determine the length of an open organ pipe that emits middle C (262 Hz) when the temperature is 18°C. (b) What are the wavelength and frequency of the fundamental standing wave in the tube? (c) What are and f in the traveling sound wave produced in the outside air?

Problem 35P (II) An organ is in tune at 22.0°C. By what percent will the frequency be off at 11°C?

(II) How far from the mouthpiece of the flute in Example 12–11 should the hole be that must be uncovered to play F above middle C at 349 Hz?

Problem 37P (II) (a) At t = 22 ° c, how long must an open organ pipe be to have a fundamental frequency of 294 Hz? (b) If this pipe is filled with helium, what is its fundamental frequency?

(II) A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe?

(II) A uniform narrow tube 1.70 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?

Problem 40P (II) A pipe in air at 23.0°C is to be designed to produce two successive harmonics at 280 Hz and 320 Hz. How long must the pipe be, and is it open or closed?

Problem 41P (II) How many overtones are present within the audible range for a 2.18-m-long organ pipe at 20°C (a) if it is open, and (b) if it is closed?

Problem 42P (II) Determine the fundamental and first overtone frequencies when you are in a 9.0-m-long hallway with all doors closed. Model the hallway as a tube closed at both ends.

(III) When a player’s finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string’s fundamental frequency (see Fig. 12–36). The string’s tension and mass per unit length remain unchanged. If the unfingered length of the string is \(e=75.0 \mathrm{~cm}\), determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note compared to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is \(2^{1 / 12}\). Equation transcription: Text transcription: e=75.0{~cm} 2^{1 / 12}

(III) The human ear canal is approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6?

(II) Approximately what are the intensities of the first two overtones of a violin compared to the fundamental? How many decibels softer than the fundamental are the first and second overtones? (See Fig. 12–15.)

Problem 46P (I) A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one of which is sounding 350 Hz. How far off in frequency is the other string?

(I) A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If humans can hear neither whistle when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.

Problem 48P (II) What is the beat frequency if middle C (262 Hz) and C# (277 Hz) are played together? What if each is played two octaves lower (each frequency reduced by a factor of 4)?

Problem 49P (II) A guitar string produces 3 beats/s when sounded with a 350-Hz tuning fork and 8 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.

Problem 50P (II) Two violin strings are tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.5%. What will be the beat frequency heard when the two strings are played together?

Problem 51P (II) The two sources of sound in Fig. 12–16 face each other and emit sounds of equal amplitude and equal frequency (305 Hz) but 180° out of phase. For what minimum separation of the two speakers will there be some point at which (a) complete constructive interference occurs and (b) complete destructive interference occurs. (Assume T = 20°C.)

Problem 52P (II) Two piano strings are supposed to be vibrating at 220 Hz, but a piano tuner hears three beats every 2.5 s when they are played together. (a) If one is vibrating at 220.0 Hz, what must be the frequency of the other (is there only one answer)? (b) By how much (in percent) must the tension be increased or decreased to bring them in tune?

Problem 53P (III) Two loudspeakers are 1.60 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. (a)What is the lowest frequency at which destructive interference will occur at this point if the speakers are in phase? (b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20° C.

(III) Two loudspeakers are placed 3.00 m apart, as shown in Fig. 12–37. They emit 474-Hz sounds, in phase. A microphone is placed 3.20 m distant from a point midway between the two speakers, where an intensity maximum is recorded. (a) How far must the microphone be moved to the right to find the first intensity minimum? (b) Suppose the speakers are reconnected so that the 474-Hz sounds they emit are exactly out of phase. At what positions are the intensity maximum and minimum now?

Problem 55P (III) A source emits sound of wavelengths 2.54 m and 2.72 m in air. (a) How many beats per second will be heard? (Assume T = 20°C ) (b) How far apart in space are the regions of maximum intensity?

Problem 56P (I) The predominant frequency of a certain fire truck’s siren is 1650 Hz when at rest. What frequency do you detect if you move with a speed of 30.0 m/s (a) toward the fire truck, and (b) away from it?

Problem 57P (II) A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 27.5 m/s What is the received sound frequency?

Problem 58P (II) Two automobiles are equipped with the same single-frequency horn. When one is at rest and the other is moving toward the first at 18 m/s, the driver at rest hears a beat frequency of 4.5 Hz. What is the frequency the horns emit? Assume T =20° C.

Problem 59P (II) As a bat flies toward a wall at a speed of 6.0 m/s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?

Problem 60P (II) In one of the original Doppler experiments, a tuba was played at a frequency of 75 Hz on a moving flat train car, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard in the station if the train car approached the station at a speed of 14.0 m/s ?

Problem 61P (II) A wave on the ocean surface with wavelength 44 m travels east at a speed of 18m/s relative to the ocean floor. If, on this stretch of ocean, a powerboat is moving at 14 m/s (relative to the ocean floor), how often does the boat encounter a wave crest, if the boat is traveling (a) west, and (b) east?

Problem 62P (III) A police car sounding a siren with a frequency of 1580 Hz is traveling at 120.0 km/h. (a) What frequencies does an observer standing next to the road hear as the car approaches and as it recedes? (b) What frequencies are heard in a car traveling at 90.0 km/h in the opposite direction before and after passing the police car? (c) The police car passes a car traveling in the same direction at 80.0 km/h. What two frequencies are heard in this car?

Problem 63P (III) The Doppler effect using ultrasonic waves of frequency 2.25 X 106 Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 240 Hz is observed. Assuming that the speed of sound in tissue is 1540 m/s, calculate the maximum velocity of the surface of the beating heart.

Problem 64P (I) (a) How fast is an object moving on land if its speed at 24°C is Mach 0.33? (b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.1 on a screen. What is the speed of sound at that altitude?

Problem 65P (I) The wake of a speedboat is 12° in a lake where the speed of the water wave is 2.2 km/h. What is the speed of the boat?

Problem 66P (II) An airplane travels at Mach 2.1 where the speed of sound Is 310 m/s. (a) What is the angle the shock wave makes with the direction of the airplane’s motion? (b) If the plane is flying at a height of 6500 m, how long after it is directly overhead will a person on the ground hear the shock wave?

Problem 67P (II) A space probe enters the thin atmosphere of a planet where the speed of sound is only about 42 m/s. (a) What is the probe’s Mach number if its initial speed is (b) What is the angle of the shock wave 15,000 km/h? relative to the direction of motion?

Problem 68P (II) A meteorite traveling 9200 m/s strikes the ocean. Determine the shock wave angle it produces (a) in the air just before entering the ocean, and (b) in the water just after entering. Assume T =20° C.

(III) You look directly overhead and see a plane exactly 1.45 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–38. Determine (a) the angle of the shock cone, ,and (b) the speed of the plane and its Mach number. Assume the speed of sound is 330 m/s.

(III) A supersonic jet traveling at Mach 2.0 at an altitude of 9500 m passes directly over an observer on the ground. Where will the plane be relative to the observer when the latter hears the sonic boom? (See Fig. 12–39.)

Problem 71 GP A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 85 m, what is the minimum time between pulses (in fresh water)?

Problem 72GP A single mosquito 5.0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 200 such mosquitoes?

Problem 73GP What is the resultant sound level when an 81-dB sound and an 87-dB sound are heard simultaneously?

Problem 74GP The sound level 8.25 m from a loudspeaker, placed in the open, is 115 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?

Problem 75GP A stereo amplifier is rated at 225 W output at 1000 Hz. The power output drops by 12 dB at 15 kHz. What is the power output in watts at 15 kHz?

Problem 76GP Workers around jet aircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 130 dB, and that the average human ear has an effective radius of 2.0 cm.What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?

In audio and communications systems, the gain, \(\beta\), in decibels is defined for an amplifier as \(\beta=10 \log \left(\frac{P_{\text {out }}}{P_{\text {in }}}\right)\) Equation transcription: Text transcription: beta beta=10 \log(rac{P{ {out }}}{P{ {in }}})

Manufacturers typically offer a particular guitar string in a choice of diameters so that players can tune their instruments with a preferred string tension. For example, a nylon high-E string is available in a low- and high-tension model with diameter 0.699 mm and 0.724 mm, respectively. Assuming the density of nylon is the same for each model, compare (as a ratio) the tension in a tuned high- and low-tension string.

Problem 79GP A tuning fork is set into vibration above a vertical open tube filled with water (Fig. 12–40). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?

Problem 80GP Two identical tubes, each closed at one end, have a fundamental frequency of 349 Hz at 25.0°C. The air temperature is increased to 31.0°C in one tube. If the two pipes are now sounded together, what beat frequency results?

Each string on a violin is tuned to a frequency \(1 \frac{1}{2}\) times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string? Equation transcription: Text transcription: 1 frac{1}{2}

Problem 82P A particular whistle produces sound by setting up the fundamental standing wave in an air column 7.10 cm long. The tube is closed at one end. The whistle blower is riding in a car moving away from you at 25 m/s. What frequency do you hear?

Problem 83GP The diameter D of a tube does affect the node at the open end of a tube. The end correction can be roughly approximated as adding D/3 to to give us an effective length for the tube in calculations. For a closed tube of length 0.55 m and diameter 3.0 cm, what are the frequencies of the first four harmonics, taking the end correction into consideration?

Problem 84GP The frequency of a steam train whistle as it approaches you is 565 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?

Problem 85GP Two trains emit 508-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.5-Hz beat frequency when the other train approaches. What is the speed of the moving train?

Two loudspeakers are at opposite ends of a railroad car as it moves past a stationary observer at 12.0 m/s, as shown in Fig. 12–41. If the speakers have identical sound frequencies of 348 Hz, what is the beat frequency heard by the observer when (a) he listens from position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

Problem 87GP Two open organ pipes, sounding together, produce a beat frequency of 6.0 Hz. The shorter one is 2.40 m long. How long is the other?

Problem 88GP A bat flies toward a moth at 7.8 m/s speed while the moth is flying toward the bat at speed 5.0 m/s.The bat emits a sound wave of 51.35 kHz.What is the frequency of the wave detected by the bat after that wave reflects off the moth?

Problem 89GP A bat emits a series of high-frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one pulse returns before the next pulse is emitted?

Problem 90GP Two loudspeakers face each other at opposite ends of a long corridor. They are connected to the same source which produces a pure tone of 282 Hz. A person walks from one speaker toward the other at a speed of 1.6 m/s. What “beat” frequency does the person hear?

Problem 91GP A sound-insulating door reduces the sound level by 30 dB. What fraction of the sound intensity passes through this door?

The “alpenhorn” (Fig. 12–42) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the \(\mathrm F^{\#}\) (or \(\mathrm G^\flat\)) horn. What is the fundamental frequency of this horn, and which overtone is close to \(\mathrm F^{\#}\)? (See Table 12–3.) Model as a tube open at both ends.

Problem 93GP Room acoustics for stereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 4.7 m long, 3.6 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room

Problem 94GP A dramatic demonstration, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For an 80-cm-long rod, (a) what is the fundamental frequency of the sound? (b) What is its wavelength in the rod, and (c) what is the traveling wavelength of the sound in air at 20°C?

The intensity at the threshold of hearing for the human ear at a frequency of about 1000 Hz is \(I_{0}=1.0 x 10^{-12} W / m^{2}\) for which \(\beta\), the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or \(I=1.0 \mathrm{~W} / \mathrm{m}^{2}\) corresponding to an increase of intensity by a factor of 1012 By what factor does the displacement amplitude, , vary? Equation transcription: Text transcription: I{0}=1.0 x 10^{-12} W / m^{2} beta I=1.0{~W} /{m}^{2}

Problem 96GP A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is about 1540 m/s. What is the expected beat frequency if blood is flowing in large leg arteries at 3.0 cm/s directly away from the sound source?

A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.5 s after shouting. Estimate the length of the lake.

A sailor strikes the side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.0 s later. How deep is the ocean at this point? Assume the speed of sound in sea water is (Table 121) and does not vary significantly with depth.

(a) Calculate the wavelengths in air at 20C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b) What is the wavelength of an 18-MHz ultrasonic wave?

On a warm summer day (31C), it takes 4.80 s for an echo to return from a cliff across a lake. On a winter day, it takes 5.20 s. What is the temperature on the winter day?

An ocean fishing boat is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.55 km away (Fig. 1233). How much time elapses before the backfire is heard (a) by the fish, and (b) by the fishermen?

A person, with his ear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 0.80 s apart. How far away did the impact occur? See Table 121.

(III) A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 2.7 s later. How high is the cliff?

What is the intensity of a sound at the pain level of 120 dB? Compare it to that of a whisper at 20 dB

What is the sound level of a sound whose intensity is 1.5 * 106 Wm2?

You are trying to decide between two new stereo amplifiers. One is rated at 75 W per channel and the other is rated at 120 W per channel. In terms of dB, how much louder will the more powerful amplifier be when both are producing sound at their maximum levels?

If two firecrackers produce a combined sound level of 85 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dBs.]

A person standing a certain distance from an airplane with four equally noisy jet engines is experiencing a sound level of 140 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dBs.]

One CD player is said to have a signal-to-noise ratio of 82 dB, whereas for a second CD player it is 98 dB. What is the ratio of intensities of the signal and the background noise for each device?

A 55-dB sound wave strikes an eardrum whose area is (a) How much energy is received by the eardrum per second? (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J

(II) At a rock concert, a dB meter registered 130 dB when placed 2.5 m in front of a loudspeaker on stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air? (b) How far away would the sound level be 85 dB?

A fireworks shell explodes 100 m above the ground, creating colorful sparks. How much greater is the sound level of the explosion for a person at a point directly below the explosion than for a person a horizontal distance of 200 m away (Fig. 1234)?

If the amplitude of a sound wave is made 3.5 times greater, (a) by what factor will the intensity increase? (b) By how many dB will the sound level increase?

Two sound waves have equal displacement amplitudes, but one has 2.2 times the frequency of the other. What is the ratio of their intensities?

What would be the sound level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 440 Hz?

(a) Estimate the power output of sound from a person speaking in normal conversation. Use Table 122. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. (b) How many people would it take to produce a total sound output of 60 W of ordinary conversation? [Hint: Add intensities, not dBs.]

Expensive amplifier A is rated at 220 W, while the more modest amplifier B is rated at 45 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp. (b) Will the expensive amp sound twice as loud as the cheaper one?

A 5000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 126.)

What are the lowest and highest frequencies that an ear can detect when the sound level is 40 dB? (See Fig. 126.)

Your ears can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at (a) 100 Hz, (b) 5000 Hz? (See Fig. 126.)

Estimate the number of octaves in the human audible range, 20 Hz to 20 kHz.

What would you estimate for the length of a bass clarinet, assuming that it is modeled as a closed tube and that the lowest note that it can play is a whose frequency is 69 Hz?

The A string on a violin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has mass 0.35 g. Under what tension must the string be placed?

An organ pipe is 116 cm long. Determine the fundamental and first three audible overtones if the pipe is (a) closed at one end, and (b) open at both ends.

(a) What resonant frequency would you expect from blowing across the top of an empty soda bottle that is 24 cm deep, if you assumed it was a closed tube? (b) How would that change if it was one-third full of soda?

If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?

A tight guitar string has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 70% of its original length?

(II) Estimate the frequency of the “sound of the ocean” when you put your ear very near a 15-cm-diameter seashell (Fig. 12–35).

An unfingered guitar string is 0.68 m long and is tuned to play E above middle C (330 Hz). (a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the wavelength on the string of this 440-Hz wave? (c) What are the frequency and wavelength of the sound wave produced in air at 22C by this fingered string?

(a) Determine the length of an open organ pipe that emits middle C (262 Hz) when the temperature is 18C. (b) What are the wavelength and frequency of the fundamental standing wave in the tube? (c) What are and f in the traveling sound wave produced in the outside air?

An organ is in tune at 22.0C. By what percent will the frequency be off at 11C?

How far from the mouthpiece of the flute in Example 1211 should the hole be that must be uncovered to play F above middle C at 349 Hz?

(a) At how long must an open organ pipe be to have a fundamental frequency of 294 Hz? (b) If this pipe is filled with helium, what is its fundamental frequency? 38. (II) A particular organ pipe can resonate at 264 Hz

A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe?

A uniform narrow tube 1.70 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?

A pipe in air at 23.0C is to be designed to produce two successive harmonics at 280 Hz and 320 Hz. How long must the pipe be, and is it open or closed

How many overtones are present within the audible range for a 2.18-m-long organ pipe at 20C (a) if it is open, and (b) if it is closed?

Determine the fundamental and first overtone frequencies when you are in a 9.0-m-long hallway with all doors closed. Model the hallway as a tube closed at both ends

When a players finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the strings fundamental frequency (see Fig. 1236). The strings tension and mass per unit length remain unchanged. If the unfingered length of the string is determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note compared to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 2112.

(III) The human ear canal is approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6?

Approximately what are the intensities of the first two overtones of a violin compared to the fundamental? How many decibels softer than the fundamental are the first and second overtones? (See Fig. 1215.)

A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one of which is sounding 350 Hz. How far off in frequency is the other string?

A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If humans can hear neither whistle when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.

What is the beat frequency if middle C (262 Hz) and (277 Hz) are played together? What if each is played two octaves lower (each frequency reduced by a factor of 4)?

A guitar string produces when sounded with a 350-Hz tuning fork and when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.

Two violin strings are tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.5%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 1113.]

The two sources of sound in Fig. 1216 face each other and emit sounds of equal amplitude and equal frequency (305 Hz) but 180 out of phase. For what minimum separation of the two speakers will there be some point at which (a) complete constructive interference occurs and (b) complete destructive interference occurs. (Assume )

Two piano strings are supposed to be vibrating at 220 Hz, but a piano tuner hears three beats every 2.5 s when they are played together. (a) If one is vibrating at 220.0 Hz, what must be the frequency of the other (is there only one answer)? (b) By how much (in percent) must the tension be increased or decreased to bring them in tune?

Two loudspeakers are 1.60 m apart. A person stands 3.00 m from one speaker and 3.50 m from the other. (a) What is the lowest frequency at which destructive interference will occur at this point if the speakers are in phase? (b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest).

Two loudspeakers are placed 3.00 m apart, as shown in Fig. 1237. They emit 474-Hz sounds, in phase. A microphone is placed 3.20 m distant from a point midway between the two speakers, where an intensity maximum is recorded. (a) How far must the microphone be moved to the right to find the first intensity minimum? (b) Suppose the speakers are reconnected so that the 474-Hz sounds they emit are exactly out of phase. At what positions are the intensity maximum and minimum now?

A source emits sound of wavelengths 2.54 m and 2.72 m in air. (a) How many beats per second will be heard? (Assume ) (b) How far apart in space are the regions of maximum intensity?

The predominant frequency of a certain fire trucks siren is 1650 Hz when at rest. What frequency do you detect if you move with a speed of (a) toward the fire truck, and (b) away from it?

A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at What is the received sound frequency?

(II) Two automobiles are equipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 18 m/s, the driver at rest hears a beat frequency of 4.5 Hz. What is the frequency the horns emit? Assume \(T = 20^{\circ}C\).

(II) As a bat flies toward a wall at a speed of 6.0 m/s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?

In one of the original Doppler experiments, a tuba was played at a frequency of 75 Hz on a moving flat train car, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard in the station if the train car approached the station at a speed of 14.0 ms?

A wave on the ocean surface with wavelength 44 m travels east at a speed of relative to the ocean floor. If, on this stretch of ocean, a powerboat is moving at (relative to the ocean floor), how often does the boat encounter a wave crest, if the boat is traveling (a) west, and (b) east?

A police car sounding a siren with a frequency of 1580 Hz is traveling at (a) What frequencies does an observer standing next to the road hear as the car approaches and as it recedes? (b) What frequencies are heard in a car traveling at in the opposite direction before and after passing the police car? (c) The police car passes a car traveling in the same direction at What two frequencies are heard in this car?

The Doppler effect using ultrasonic waves of frequency is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 240 Hz is observed. Assuming that the speed of sound in tissue is calculate the maximum velocity of the surface of the beating heart

(a) How fast is an object moving on land if its speed at 24C is Mach 0.33? (b) A high-flying jet cruising at displays a Mach number of 3.1 on a screen. What is the speed of sound at that altitude?

The wake of a speedboat is 12 in a lake where the speed of the water wave is What is the speed of the boat?

An airplane travels at Mach 2.1 where the speed of sound is (a) What is the angle the shock wave makes with the direction of the airplanes motion? (b) If the plane is flying at a height of 6500 m, how long after it is directly overhead will a person on the ground hear the shock wave?

A space probe enters the thin atmosphere of a planet where the speed of sound is only about (a) What is the probes Mach number if its initial speed is (b) What is the angle of the shock wave relative to the direction of motion?

A meteorite traveling strikes the ocean. Determine the shock wave angle it produces (a) in the air just before entering the ocean, and (b) in the water just after entering. Assume T = 20C

You look directly overhead and see a plane exactly 1.45 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 1238. Determine (a) the angle of the shock cone, and (b) the speed of the plane and its Mach number. Assume the speed of sound is 330 ms.

A supersonic jet traveling at Mach 2.0 at an altitude of 9500 m passes directly over an observer on the ground. Where will the plane be relative to the observer when the latter hears the sonic boom? (See Fig. 1239.

A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 85 m, what is the minimum time between pulses (in fresh water)?

A single mosquito 5.0 m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 200 such mosquitoes?

What is the resultant sound level when an 81-dB sound and an 87-dB sound are heard simultaneously?

The sound level 8.25 m from a loudspeaker, placed in the open, is 115 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?

A stereo amplifier is rated at 225 W output at 1000 Hz. The power output drops by 12 dB at 15 kHz. What is the power output in watts at 15 kHz?

Workers around jet aircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 130 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?

In audio and communications systems, the gain, \(\beta\), in decibels is defined for an amplifier as \(\beta=10 log(\frac{P_{out}}{P_{in}})\), where \(P_{in}\) is the power input to the system and \(P_{out}\) is the power output. (a) A particular amplifier puts out 135 W of power for an input of 1.0mW. What is its gain in dB? (b) If a signal-to-noise ratio of 93 dB is specified, what is the noise power if the output signal is 10 W?

Manufacturers typically offer a particular guitar string in a choice of diameters so that players can tune their instruments with a preferred string tension. For example, a nylon high-E string is available in a low- and high-tension model with diameter 0.699 mm and 0.724 mm, respectively. Assuming the density of nylon is the same for each model, compare (as a ratio) the tension in a tuned high- and low-tension string.

A tuning fork is set into vibration above a vertical open tube filled with water (Fig. 12–40). The water level is allowed to drop slowly.As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?

Two identical tubes, each closed at one end, have a fundamental frequency of 349 Hz at 25.0C. The air temperature is increased to 31.0C in one tube. If the two pipes are now sounded together, what beat frequency results?

Each string on a violin is tuned to a frequency times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?

. A particular whistle produces sound by setting up the fundamental standing wave in an air column 7.10 cm long. The tube is closed at one end. The whistle blower is riding in a car moving away from you at What frequency do you hear?

The diameter D of a tube does affect the node at the open end of a tube. The end correction can be roughly approximated as adding to to give us an effective length for the tube in calculations. For a closed tube of length 0.55 m and diameter 3.0 cm, what are the frequencies of the first four harmonics, taking the end correction into consideration?

The frequency of a steam train whistle as it approaches you is 565 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?

Two trains emit 508-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.5-Hz beat frequency when the other train approaches. What is the speed of the moving train?

Two loudspeakers are at opposite ends of a railroad car as it moves past a stationary observer at 12.0 m/s, as shown in Fig. 12-41. If the speakers have identical sound frequencies of 348 Hz, what is the beat frequency heard by the observer when (a) he listens from position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

Two open organ pipes, sounding together, produce a beat frequency of 6.0 Hz. The shorter one is 2.40 m long. How long is the other?

A bat flies toward a moth at speed 7.8 m/s while the moth is flying toward the bat at speed 5.0 m/s. The bat emits a sound wave of 51.35 kHz.What is the frequency of the wave detected by the bat after that wave reflects off the moth?

A bat emits a series of high-frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one pulse returns before the next pulse is emitted?

Two loudspeakers face each other at opposite ends of a long corridor. They are connected to the same source which produces a pure tone of 282 Hz. A person walks from one speaker toward the other at a speed of What beat frequency does the person hear?

A sound-insulating door reduces the sound level by 30 dB. What fraction of the sound intensity passes through this door?

The alpenhorn (Fig. 1242) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the (or ) horn. What is the fundamental frequency of this horn, and which overtone is close to ? (See Table 123.) Model as a tube open at both ends.

Room acoustics for stereo listening can be compromised by the presence of standing waves, which can cause acoustic dead spots at the locations of the pressure nodes. Consider a living room 4.7 m long, 3.6 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.

A dramatic demonstration, called singing rods, involves a long, slender aluminum rod held in the hand near the rods midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to sing, or emit a clear, loud, ringing sound. For an 80-cm-long rod, (a) what is the fundamental frequency of the sound? (b) What is its wavelength in the rod, and (c) what is the traveling wavelength of the sound in air at 20C?

The intensity at the threshold of hearing for the human ear at a frequency of about 1000 Hz is for which the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or corresponding to an increase of intensity by a factor of By what factor does the displacement amplitude, A, vary?

. A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is about 1540 m/s.What is the expected beat frequency if blood is flowing in large leg arteries at directly away from the sound source?