Two sinusoidal waves with the same amplitude A and frequencyf travel in opposite

Light can pass easily through water and through air, but light will reflect from the surface of a lake. What does this te ll you about the speed of light in air and in water?

Ocean waves are partially reflected from the entrance to a harbor, where the depth of the water is suddenly less. What does this tell you about the speed of waves in water of different depths?

A string has an abmpt c hange in linear density at its midpoint so that the speed of a pulse on the left s ide is 2/3 of that on the right s ide. a. On which side is the linear density greater? Explai n. b. From which s ide would you start a pulse so that its reflection from the midpoint would not be inverted? Explain.

A guitarist fi nds that the pitch of one of her strings is s lightly fl at- the frequency is a bit too low. Should she increase or decrease the tension of the string? Explain.

Certain illnesses inflame your vocal cords, caus ing them to swell. How does this affect the pitc h of your voice? Explain.

6. Figure Ql 6.6 shows a standi ng wave on a string that is oscillating at frequency / 0 . How many antinodes will there be if the frequency is doubled to 2fo? Explain.

Figure QI 6.7 shows a standing sound wave in a tube of air that is open at both ends. a . Which mode (value of m) stand ing wave is this? b. Is the air vibrating horizontally or vertically?

A typical fl ute is about 66 cm long. A piccolo is a very similar instmment, though it is smaller, with a length of about 32 cm. How does the pitch of a piccolo compare to that of a flute?

Some pipes on a pipe organ are open at both ends, others are closed at one end. For pipes that play low-frequency notes, there is an advantage to using pipes that are closed at one end. What is the advantage?

A fri end's voice sounds different over the te lephone than it does in person. This is because te lephones do not transmit frequencies over about 3000 Hz. 3000 Hz is well above the normal frequency of speech, so why doe s eliminating these high frequencies change the sound of a person's voice?

Suppose you were to play a tmmpet after breathing helium, in which the speed of sound is much greater than in air. Would the pitch of the instmment be higher or lower than normal, or would it be unaffected by be ing played with he lium inside the tube rather than air?

If you pour liquid in a tall, narrow glass, you may hear sound with a steadi ly rising pitch. What is the source of the sound, and why does the pitch rise as the glass fills?

When you speak after breathing helium, in which the speed of sound is much greater than in air, your voice sounds qui te different. The frequencies emitted by your vocal cords do not change since they are determined by the mass and tension of your vocal cords. So what does change when your vocal tract is filled with helium rather than air?

Sopranos can s ing notes at very high frequencies-over BIO 1000 Hz. When they sing such high notes, it can be d ifficult to unders tand the words they are singing. Use the concepts of harmonics and formants to explain this.

A synthesizer is a keyboard instrument that can be made to sound like a flute, a trumpet, a piano-or any other musical instrument. Pressing a key sets the fu ndamental frequency of the note that is produced. Other settings that the player can adjust change the sound quality of the synthesizer without altering the fundamental frequency. How is this change accomplished? What is bei ng adjusted?

If a cold gives you a s tuffed-up nose, it changes the way your voice sounds, even if your vocal cords are not affected. Explain why this is so.

A small boy and a grown woman both speak at approximately the same pitch. Nonethe less, it's easy to tell which is which from listening to the sounds of their voices. How are you able to make this determination?

At I = I s, what is the displacement y of the string at x = 7 cm? A. -1.0 mm B. Omm C. 0.5 mm D. l .Omm E. 2.0 mm

At x = 3 cm, what is the earl iest time that y will equal 2 mm? A. 0.5 s B. 0.7 s C. 1.0 s D. 1.5 s E. 2.5 s

At 1= l.5s,what is thevalueof yat x = IOcm? A. - 2.0 mm B. -1.0 mm C. -0.5 mm D. Omm E. l .O mm

Two sinusoidal waves with the same amplitude A and frequency f travel in opposite directions a long a long string. You stand at one point and watch the string. The maximum displacement of the string at that point is A. A B. 2A C. 0 D. There is not enough information to decide.

A student in her physics lab measures the standing-wave modes of a tube. The lowest frequency that makes a resonance is 20 Hz. As the frequency is increased, the next resonance is at 60 Hz. W)lat will be the next resonance after this? A. 80 Hz B. JOO Hz C. 120Hz D. 180Hz

An organ pipe is tuned to exactly 384 Hz when the temperature in the room is 20C. Later, when the air has warmed up to 25C, the frequency is A. Greater than 384 Hz. B. 384 Hz. C. Less than 384 Hz.

Resonances of the ear canal lead to increased sensitivity of hearing, as we've seen. Dogs have a much longer ear canal- 5.2 cm-than humans. What are the two lowest frequencies at which dogs have an increase in sensiti vity? The speed of sound in the warm air of the ear is 350 mis. A. 1700 Hz, 3400 Hz B. 1700 Hz, 5100 Hz C. 3400 Hz, 6800 Hz D. 3400 Hz, 10,200 Hz

The frequency of the lowest standing-wave mode on a 1.0-m-long string is 20 Hz. What is the wave speed on the string? A. I 0 mis B. 20 mis C. 30 mis D. 40 mis

Suppose you pluck a string on a guitar and it produces the note A at a frequency of 440 Hz. Now you press your finger down on the string against one of the frets, making this point the new end of the string. The newly shortened string has 415 the length of the full string. When you pluck the string, its frequency will be A. 350 Hz B. 440 Hz C. 490 Hz D. 550 Hz

A drainage pipe running under a freeway is 30.0 m long. Both ends of the pipe are open, and wind blowing across one end causes the air inside to vibrate. a. If the speed of sound on a particular day is 340 mis, what wi ll be the fundamental frequency of air vibration in this pipe? b. What is the frequency of the lowest harmonic that would be audible to the human ear? c. What will happen to the frequency io the later afternoon as the air begins to cool?

Some pipe organs create sounds lower than humans can hear. This "infrasound" can still create physical sensations. What is the fundamental frequency of the sound from an open-open pipe that is 32 feel long (a common size for large organs)? Whal length open-closed tube is necessary to produce this note? Assume a sound speed of 343 m/s.

Although the vocal tract is quite complicated, we can make a simple model of it as an open-closed tube extending from the openi ng of the mouth to the diaphragm, the large muscle separating the abdomen and the chest cavity. What is the length of this tube if its fundamental frequency equals a typical speech frequency of 200 Hz? Assume a sound speed of 350 m/s. Does this result for the tube length seem reasonable, based on observations on your own body?

You know that you sound better when you sing in the shower. This has to do with the amplification of frequencies that correspond to the standing-wave resonances of the shower enclosure. A shower enclosure is created by adding glass doors and ti le walls to a standard bathtub, so the enclosure has the dimensions of a standard tub, 0.75 m wide and 1.5 m long. Standing sound waves can be set up along e ither axis of the enclosure. What are the lowest two frequencies that correspond to resonances on each axis of the shower? These frequencies will be especially amplified. Assume a sound speed of 343 mis.

A child has an ear canal that is 1.3 cm long. At what sound BIO frequencies in the audible range will the child have increased hearing sensitivity?

When a sound wave travels directly toward a hard wall, the incoming and reflected waves can combine to produce a standing wave. There is an antinode right at the wall, just as at the end of a closed tube, so the sound near the wall is loud. You are standing beside a brick wall listening to a 50 Hz tone from a distant loudspeaker. How far from the wall mu t you move to find the fi rst quiet spot? Assume a sound speed of 340 mis.

The fi rsl formant of your vocal system can be modeled as the resonance of an open-closed tube, the closed end being your vocal cords and the open end your lips. Estimate the frequency of the first formant from the graph of Figure 16.23, and then estimate the length of the tube of which this is a resonance. Does your result seem reasonable?

When you voice the vowel sound in "hat," you narrow the opening whe re your throat opens into the cavity of your mouth so that your vocal tract appears as two connected tubes. The fi rst is in your throat, closed at the vocal cords and open at the back of the mouth. T he second is the mouth itself, open at the lips and closed at the back of the mouth-a diffe rent condition than for the throat because of the re latively larger size of the cavity. The corresponding formant frequencies are 800 Hz (for the throat) and 1500 Hz (for the mouth). What are the lengths of these two ca vities? Assume a sound speed of 350 mis.

The first and second formants when you make an "ee" vowel sound are approximately 270 Hz and 2300 Hz. The speed of sound in your vocal tract is approximate ly 350 mis. If you breathe a mix of oxygen and helium (as deep-sea divers often do), the speed increases to 750 mis. With this mix of gases, what are the frequencies of the two formants?

Two loudspeakers in a 20C room emit 686 Hz sound waves along the x-axis. What is the smallest distance between the speakers for which the interference of the sound waves is destructive?

Two loudspeakers emit sound waves a long the x-axi s. The sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is inc reased, reaching zero at a se paration of 30 cm. a. What is the wavelength of the sound? b. If the distance between the speakers conti nues to increase, at what separation will the sound intensity again be a maximum?

In noisy fac tory environments, it's possible to use a loudspeaker to cancel persistent low-frequency machine noise at the position of one worker. The details of practical systems are complex, but we can present a simple example that gives you the idea. Suppose a machine 5.0 m away from a worker emits a persistent 80 Hz hum. To cancel the sound at the worker's location with a speaker that exactly duplicates the machine's hum, how far from the worker should the speaker be placed? Assume a sound speed of 340 mis.

Two identical loudspeake rs separated by distance d emit 170 Hz sound waves along the x-axis. As you walk a long the axis, away from the speakers, you don't hear anythi ng even though both speakers are on. What are three possible values for d? Assume a sound speed of 340 mis.

Figure PJ 6.40 shows the circular wave fronts emitted by two sources. Make a table with rows labeled P, Q, and R and columns labeled ri. 'i , 6. r, and Cl D. Fi II in the table for points P, Q, and R, giving the distances as multiples of A and indicati ng, with a C or a D, whether the i nterference at that point is constructive Problems 527 or destructi ve.

Two identical loudspeakers 2.0 m apart are emitting 1800 Hz sound waves into a room where the speed of sound is 340 mis. Is the point 4.0 m directly in front of one of the speakers, perpendicular to the plane of the speakers, a point of maximum constructive inte1fere nce, perfect destructive interference, or something in between?

An engine whose sparkplugs fire 120 times a second generates noise at 120 Hz. The sound level can be reduced by fitting the engine with an exhaust resonator that cancels this primary "note." The resonator is an open-closed tube, with the open end connected to the exhaust system. Sound enters the tube, reflects from the closed end, and re-enters the exhaust system exactly out of phase with the incoming sound. How Jong must the tube be? Assume a sound speed of 360 mis in the wam1 exhaust gases.

Musicians can use beats to tune their instruments. One flu te is properly tuned and plays the musical note A at exactly 440 Hz. A second player sounds the same note and hears that her instrument is slightly " fl at" (that is, at too low a frequency). Playing at the same time as the first fl ate, she hears two loud-soft-loud beats per second. What is the freque ncy of her instrument?

A student waiting at a stoplight notices that her tum signal, which has a period of0.85 s, makes one blink exactly in sync with the tum signal of the car in front of her. The blinker of the car ahead then starts to get ahead, but 17 s later the two are exactly in sync again. What is the period of the blinker of the other car?

Two strings are adjusted to vibrate at exactly 200 Hz. Then the tension in one string is increased slightly. Afterward, three beats per second are heard when the strings vibrate at Lhe same time. What is the new frequency of the string that was tightened?

A child's Lrain whistle replicates a classic conductor's whistle from the early 1900s. This whistle has two open-open tubes that produce two different frequencies. When you hear these two different frequencies simultaneously, you may have the perception of also hearing a lower note, called a dijj"ere11ce tone, that is at the same frequency as the beat frequency between the two notes. The two tubes of the whi stle are I 2cm and 11 cm in length. Assuming a sound speed of 350 mis, what is the frequency of this dif'forence tone?

A flute player hears four beats per second when she compares her note to a 523 Hz tuning fork (the note C). She can match the frequency of the tuning fork by pull ing out the "tuning joint" to lengthen her fl ute slightly. What was her ini tial frequency?

The fundamental freq uency of a standing wave on a 1.0-m-long string is 440 Hz. What would be the wave speed of a pulse moving along this string?

In addition to producing images, ultrasound can be used to heat tissues of the body for therapeutic purposes. An emitter is placed against the sutface of the skin; the amplitude of the ultrasound wave at this poi nt is quite large. When a sound wave hits the boundary between soft t.issue and bone, most of the e nergy is reflected. The bounda1y acts like the closed end of a tube, which can lead to standing waves. Suppose 0.70 MHz ultrasound is directed through a layer of tissue with a bone 0.55 cm below the surface. Will standing waves be created? Explain.

An 80-cm-long steel string with a linear density of 1.0 g/m is under 200 N te nsion. It is plucked and vibrates at its fundamental frequency. What is the wavelength of the sound wave that reaches your ear in a 20C room?

Tendons are, essentia lly, e lastic cords stretched between two fixed ends; as such, they can support standing waves. These resonances can be undesirable. The Achilles tendon connects the heel with a muscle in the calf. A woma n bas a 20-cm-long tendon with a cross-sect.ion area of 110 mm2. The densi ty of tendon tissue is 1100 kg/m3 For a reasonable tension of 500 N, what will be the resonant frequenc ies of her Achilles tendon?

A string, stretched between two fixed posts, forms standingwave resonances at 325 Hz and 390 Hz. What is the largest possible value of its fundamental frequency?

Spiders may "tune" strands of their webs to give enhanced BIO response at frequencies corresponding to the frequencies at INT which desirable prey might struggle. Orb web silk has a typical diameter of 0.0020 mm, and spider si lk has a density of 1300 kg/m3 . To give a resonance at I 00 Hz, to what tension must a spider adjust a 12-cm-long strand of si lk?

A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39. I cm. The room is slightly warm, so the speed of sound is 344 m/s. If the string's linear density is 0.600 g/m and the tension is 150 N, how long is the vibrating section of the violin string?

A 12 kg hanging sculpture is suspended by a 90-cm-long, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency. What is the frequency of the hum?

Lake Erie is prone to remarkable seiches-standing waves that slosh water back and forth in the lake basin from the west end at Toledo to the east end at Buffalo. Figure P l6.56 shows smoothed data for the displacement from normal water levels along the lake at the high point of one particular seiche. 3 hours later the water was at normal levels throughout the basin; 6 hours later the water was high in Toledo and low in Buffalo. a. What is the wavelength of this standing wave? b. What is the frequency? c. What is the wave speed?

A microwave generator can produce microwaves at any frequency between 10 GHz and 20 GHz. As Figure P 16.57 shows, the microwaves are aimed, through a small hole, into a "microwave cavity" that consists of a IO-cm-long cylinder with retlect.ive ends. a. Which frequencies between lO GHz and 20 GHz will create standing waves in the microwave cavity? b. For which of these frequencies is the cavity midpoint an anti node?

A carbon-dioxide laser emits infrared light with a wavelength of 10.6 m. a. What is the length of a tube that wi ll oscillate in the m = 100,000 mode? b. What is the frequency? c. Imagine a pulse of li ght bouncing back and fo rth between the ends of the tube. How many round trips will the pulse make in each second?

A 40-cm-long tube has a 40-cm long inse rt that can be pulled in and ~ out, as shown in Figure P I6.59. A vibrating tuning fork is held next to the tube. As the insert is slowly pulled out, the sound from the tuning fork creates standing waves in the tube when the total length l is 42.5 cm, 56.7 cm, and 70 .9 cm. What is the frequency of the tuning fork? The air temperature is 20C.

The width of a partic ular microwave oven is exactly right to support a standing-wave mode. Measureme nts of the temperature across the oven show that there are cold spots at each edge of the oven and at three spots in between. The wavelength of the microwaves is 12 cm. How wide is the oven?

Two loudspeakers located along the x-axis as shown in Figure Pl6.61 produce Speaker I is at the origin, while the location of speaker 2 can be varied by a remote control wielded by the listener. He notices maxima in the sound intensity when speaker 2 is located at x = 0.75 m and 1.00 m, but at no points in between. What is the freque ncy of the sound? Assume the speed of sound is 340 mis.

Two loudspeakers 42.0 m apart and facing each other emit identical 115 Hz sinusoidal sound waves in a room where the sound speed is 345 m/s. Susan is walking along a line between the speakers. As she wal ks, she finds herself moving through loud and quiet spots. If Susan stands 19.5 m from one speaker, is she standing at a quiet spot or a loud spot?

You arestanding2.50mdirectly in front of one of the two loud- speakers shown in Figure P l6.63. They are 3.00 m apart and both are playing a 686 Hz tone in phase. As you begi n to walk directly away from the speaker, at what distances from the speaker do you hear a minimum sound intensity? The room temperature is 20C.

Two loudspeakers, 4 .0 m apart and facing each other, play identical sounds of the same frequency. You stand halfway between them, where there is a maximum of sound intensity. Moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.25 m. a. What is the frequency of the sound? b. If the frequency is then increased while you remain 0.25 m from the center, what is the fi rst freque ncy for which that location wi ll be a maximum of sound intensity?

Piano tuners tune pianos by listening to the beats between the harmonics of two different st1i ngs. When properly tuned, the note A should have the frequency 440 Hz and the note E should be at 659 Hz. The tuner can determine this by listening to the beats between the third harmonic of the A and the second harmonic of the E. A tuner first tunes the A string very precisely by matching it to a 440 Hz tuning fork. She then strikes the A and E strings simultaneously and listens for beats between the hannonics. Wharbeat frequency indicates that the E string is properly tuned?

A flutist assembles her flute in a room where the speed of sound is 342 mis. When she plays the note A, it is in perfect tune with a 440 Hz tuning fork. After a few minutes, the air inside her flute has warmed to w~ere tbe speed of sound is 346 m/s. a. How many beats per second will she hear if she now plays the note A as the tuning fork is sounded? b. How far does she need to extend the "tuning joint" of her flute to be in tune with the tuning fork?

Police radars dete1mine speed by measuring the Doppler shift of radio waves reflected by a moving vehicle. They do so by determining the beat frequency between the reflected wave and the I 0.5 GHz emitted wave. Some unit~ can be calibrated by using a tuning fork; holding a vibrating fork in front of the unit causes the display to register a speed corresponding to the vibration frequency. A tuning fork is labeled "55 mph." What is the frequency of the tuning fork?

A Doppler blood flowmeter emits ultrasound at a frequency of 5.0 MHz. What is the beat frequency between the emitted waves and the waves reflected from blood cells moving away from the emitter at 0.1 5 m/s?

An ultrasound unit is being used to measure a patient's heart beat by combining the emitted 2.0 MHz signal with the sound waves re flected from the moving tissue of one point on the heart. The beat frequency between the two signals has a maximum value of 520 Hz. What is the maximum speed of the heart tissue?

What is the beat frequency between the second harmonic of G and the th ird harmonic of C? A. I Hz B. 2 Hz C. 4 Hz D. 6 Hz

Would a G-flat (frequency 370 Hz) and a C played together be consonant or dissonant? A. Consonant B. Dissonant

An organ pipe open at both ends is tuned so that its fundamental frequency is a G. How long is the pipe? A. 43 cm B. 87 cm C. 130 cm D. 173 cm

lf the C were played on an organ pipe that was open at one end and closed at the other, which of the harmonic frequencies in Figure Pl 6.70 would be present? A. All of the harmonics in the figure would be present. B. 262, 786, and 13 10 Hz C. 524, I 048, and 1572 Hz D. 262, 524, and 1048 Hz