Solved: Two trains on separate tracks move toward each

A sound wave traveling in air has a frequency f and wavelength l. A second sound wave traveling in air has wavelength l/2. What is the frequency of the second sound wave? (a) 4f (b) 2f (c) f (d) 12 f (e) 14 f

The temperature at Furnace Creek in Death Valley reached 134F on July 10, 1913. What is the speed of sound in air at this temperature? (a) 321 m/s (b) 343 m/s (c) 364 m/s (d) 375 m/s (e) 405 m/s

Ethyl alcohol has a density of 0.806 3 103 kg/m3 and a bulk modulus of 1.0 3 109 Pa. Compute the speed of sound in ethyl alcohol. (a) 1 100 m/s (b) 340 m/s (c) 820 m/s (d) 450 m/s (e) 1 300 m/s

Considering the footnote following Table 14.1, what is the speed of a longitudinal wave in a thin, solid aluminum rod? (a) 340 m/s (b) 570 m/s (c) 1 400 m/s (d) 3 200 m/s (e) 5 100 m/s

The sound intensity level of a jet plane going down the runway as observed from a certain location is 105 dB. What is the intensity of the sound at this location? (a) 2.45 3 1022 W/m2 (b) 3.54 3 1023 W/m2 (c) 8.25 3 1023 W/m2 (d) 3.16 3 1022 W/m2 (e) 1.05 3 1022 W/m2

A point source broadcasts sound into a uniform medium. If the distance from the source is tripled, how does the intensity change? (a) It becomes one ninth as large. (b) It becomes one-third as large. (c) It is unchanged. (d) It becomes three times larger. (e) It becomes nine times larger.

If a 1.00-kHz sound source moves at a speed of 50.0 m/s toward a listener who moves at a speed of 30.0 m/s in a direction away from the source, what is the apparent frequency heard by the listener? (The speed of sound is 343 m/s.) (a) 796 Hz (b) 949 Hz (c) 1 000 Hz (d) 1 070 Hz (e) 1 270 Hz

What happens to a sound wave when it travels from air into water? (a) Its intensity increases. (b) Its wavelength decreases. (c) Its frequency increases. (d) Its frequency remains the same. (e) Its velocity decreases.

When two tuning forks are sounded at the same time, a beat frequency of 5 Hz occurs. If one of the tuning forks has a frequency of 245 Hz, what is the frequency of the other tuning fork? (a) 240 Hz (b) 242.5 Hz (c) 247.5 Hz (d) 250 Hz (e) More than one answer could be correct.

A flute has a length of 58.0 cm. If the speed of sound in air is 343 m/s, what is the fundamental frequency of the flute, assuming it is a tube closed at one end and open at the other? (a) 148 Hz (b) 296 Hz (c) 444 Hz (d) 591 Hz (e) None of those answers.

The fundamental frequency of a resonating pipe is 150 Hz, and the next higher resonant frequencies are 300 Hz and 450 Hz. From this information, what can you conclude? (a) The pipe is open at one end and closed at the other. (b) The pipe could be open at each end or closed at each end. (c) The pipe must be open at each end. (d) The pipe must be closed at each end. (e) The pipe is open at both ends for the lowest frequency, only.

As you travel down the highway in your car, an ambulance approaches you from the rear at a high speed sounding its siren at a frequency of 500 Hz. Which statement is correct? (a) You hear a frequency less than 500 Hz. (b) You hear a frequency equal to 500 Hz. (c) You hear a frequency greater than 500 Hz. (d) You hear a frequency greater than 500 Hz, whereas the ambulance driver hears a frequency lower than 500 Hz. (e) You hear a frequency less than 500 Hz, whereas the ambulance driver hears a frequency of 500 Hz.

Two sirens A and B are sounding so that the frequency from A is twice the frequency from B. Compared with the speed of sound from A, is the speed of sound from B (a) twice as fast, (b) half as fast, (c) four times as fast, (d) one-fourth as fast, or (e) the same?

A hollow pipe (such as an organ pipe open at both ends) is made to go into resonance at frequency fopen. One end of the pipe is now covered and the pipe is again made to go into resonance, this time at frequency fclosed. Both resonances are first harmonics. How do these two resonances compare? (a) They are the same. (b) fopen 5 2fclosed (c) fclosed 5 2fopen (d) fopen 5 fclosed (e) fclosed 5 32 fopen

Doubling the power output from a sound source emitting a single frequency will result in what increase in decibel level? (a) 0.50 dB (b) 2.0 dB (c) 3.0 dB (d) 4 dB (e) above 20 dB

A trumpet creates a sound intensity level of 1.15 3 102 dB at a distance of 1.00 m. (a) What is the sound intensity of a trumpet at this distance? (b) What is the sound intensity of five trumpets at this distance? (c) Find the sound intensity of five trumpets at the location of the first row of an audience, 8.00 m away, assuming, for simplicity, the sound energy propagates uniformly in all directions. (d) Calculate the decibel level of the five trumpets in the first row. (e) If the trumpets are being played in an outdoor auditorium, how far away, in theory, can their combined sound be heard? (f) In practice such a sound could not be heard once the listener was 23 km away. Why cant the sound be heard at the distance found in part (e) Hint: In a very quiet room the ambient sound intensity level is about 30 dB.

There is evidence that elephants communicate via infrasound, generating rumbling vocalizations as low as 14 Hz that can travel up to 10 km. The intensity level of these sounds can reach 103 dB, measured a distance of 5.0 m from the source. Determine the intensity level of the infrasound 10 km from the source, assuming the sound energy radiates uniformly in all directions.

A family ice show is held at an enclosed arena. The skaters perform to music playing at a level of 80.0 dB. This intensity level is too loud for your baby, who yells at 75.0 dB. (a) What total sound intensity engulfs you? (b) What is the combined sound level?

A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of 50 dB by an observer 10 km away. (a) What is the average power generated by the horn? (b) What intensity level of the horns sound is observed by someone waiting at an intersection 50 m from the train? Treat the horn as a point source and neglect any absorption of sound by the air.

An outside loudspeaker (considered a small source) emits sound waves with a power output of 100 W. (a) Find the intensity 10.0 m from the source. (b) Find the intensity level in decibels at that distance. (c) At what distance would you experience the sound at the threshold of pain, 120 dB?

Show that the difference in decibel levels b1 and b2 of a sound source is related to the ratio of its distances r1 and r2 from the receivers by the formula b2 2 b1 5 20 loga r1 r2 b

A skyrocket explodes 100 m above the ground (Fig. P14.22). Three observers are spaced 100 m apart, with the first (A) directly under the explosion. (a) What is the ratio of the sound intensity heard by observer A to that heard by observer B? (b) What is the ratio of the intensity heard by observer A to that heard by observer C?

A commuter train passes a passenger platform at a constant speed of 40.0 m/s. The train horn is sounded at its characteristic frequency of 320 Hz. (a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? (b) What wavelength is detected by a person on the platform as the train approaches?

An airplane traveling at half the speed of sound emits a sound of frequency 5.00 kHz. At what frequency does a stationary listener hear the sound (a) as the plane approaches? (b) After it passes?

Two trains on separate tracks move toward each other. Train 1 has a speed of 130 km/h; train 2, a speed of 90.0 km/h. Train 2 blows its horn, emitting a frequency of 500 Hz. What is the frequency heard by the engineer on train 1?

At rest, a cars horn sounds the note A (440 Hz). The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one-third the cars speed hears a frequency of 415 Hz. (a) Is the cyclist ahead of or behind the car? (b) What is the speed of the car?

An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 465 Hz when the train is approaching him and 441 Hz when the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find?

A bat flying at 5.00 m/s is chasing an insect flying in the same direction. If the bat emits a 40.0-kHz chirp and receives back an echo at 40.4 kHz, (a) what is the speed of the insect? (b) Will the bat be able to catch the insect? Explain.

A tuning fork vibrating at 512 Hz falls from rest and accelerates at 9.80 m/s2. How far below the point of release is the tuning fork when waves of frequency 485 Hz reach the release point?

Expectant parents are thrilled to hear their unborn babys heartbeat, revealed by an ultrasonic motion detector. Suppose the fetuss ventricular wall moves in simple harmonic motion with amplitude 1.80 mm and frequency 115 beats per minute. The motion detector in contact with the mothers abdomen produces sound at precisely 2 MHz, which travels through tissue at 1.50 km/s. (a) Find the maximum linear speed of the heart wall. (b) Find the maximum frequency at which sound arrives at the wall of the babys heart. (c) Find the maximum frequency at which reflected sound is received by the motion detector. (By electronically listening for echoes at a frequency different from the broadcast frequency, the motion detector can produce beeps of audible sound in synchrony with the fetal heartbeat.)

A supersonic jet traveling at Mach 3.00 at an altitude of h 5 20 000 m is directly over a person at time t 5 0 as shown in Figure P14.31. Assume the average speed of sound in air is 335 m/s over the path of the sound. (a) At what time will the person encounter the shock wave due to the sound emitted at t 5 0? (b) Where will the plane be when this shock wave is heard?

A yellow submarine traveling horizontally at 11.0 m/s uses sonar with a frequency of 5.27 3 103 Hz. A red submarine is in front of the yellow submarine and moving 3.00 m/s relative to the water in the same direction. A crewman in the red submarine observes sound waves (pings) from the yellow submarine. Take the speed of sound in seawater as 1 533 m/s. (a) Write Equation 14.12. (b) Which submarine is the source of the sound? (c) Which submarine carries the observer? (d) Does the motion of the observers submarine increase or decrease the time between the pressure maxima of the incoming sound waves? How does that affect the observed period? The observed frequency? (e) Should the sign of v0 be positive or negative? (f) Does the motion of the source submarine increase or decrease the time observed between the pressure maxima? How does this motion affect the observed period? The observed frequency? (g) What sign should be chosen for vs? (h) Substitute the appropriate numbers and obtain the frequency observed by the crewman on the red submarine.

Two small speakers are driven by a common oscillator at 8.00 3 102 Hz. The speakers face each other and are separated by 1.25 m. Locate the points along a line joining the two speakers where relative minima would be expected. (Use v 5 343 m/s.)

The acoustical system shown in Figure P14.34 is driven by a speaker emitting sound of frequency 756 Hz. (a) If constructive interference occurs at a particular instant, by what minimum amount should the path length in the upper U-shaped tube be increased so that destructive interference occurs instead? (b) What minimum increase in the original length of the upper tube will again result in constructive interference?

The ship in Figure P14.35 travels along a straight line parallel to the shore and a distance d 5 600 m from it. The ships radio receives simultaneous signals of the same frequency from antennas A and B, separated by a distance L 5 800 m. The signals interfere constructively at point C, which is equidistant from A and B. The signal goes through the first minimum at point D, which is directly outward from the shore from point B. Determine the wavelength of the radio waves.

Two loudspeakers are placed above and below each other, as in Figure P14.36 and driven by the same source at a frequency of 4.50 3 102 Hz. An observer is in front of the speakers (to the right) at point O, at the same distance from each speaker. What minimum vertical distance upward should the top speaker be moved to create destructive interference at point O?

A pair of speakers separated by a distance d 5 0.700 m are driven by the same oscillator at a frequency of 686 Hz. An observer originally positioned at one of the speakers begins to walk along a line perpendicular to the line joining the speakers as in Figure P14.37. (a) How far must the observer walk before reaching a relative maximum in intensity? (b) How far will the observer be from the speaker when the first relative minimum is detected in the intensity?

A steel wire in a piano has a length of 0.700 0 m and a mass of 4.300 3 1023 kg. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle C (fC 5 261.6 Hz on the chromatic musical scale)?

A stretched string fixed at each end has a mass of 40.0 g and a length of 8.00 m. The tension in the string is 49.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (b) What is the vibration frequency for this harmonic?

How far, and in what direction, should a cellist move her finger to adjust a strings tone from an out-of-tune 449 Hz to an in-tune 440 Hz? The string is 68.0 cm long, and the finger is 20.0 cm from the nut for the 449-Hz tone.

A stretched string of length L is observed to vibrate in five equal segments when driven by a 630-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in three segments?

Two pieces of steel wire with identical cross sections have lengths of L and 2L. The wires are each fixed at both ends and stretched so that the tension in the longer wire is four times greater than in the shorter wire. If the fundamental frequency in the shorter wire is 60 Hz, what is the frequency of the second harmonic in the longer wire?

A steel wire with mass 25.0 g and length 1.35 m is strung on a bass so that the distance from the nut to the bridge is 1.10 m. (a) Compute the linear density of the string. (b) What velocity wave on the string will produce the desired fundamental frequency of the E1 string, 41.2 Hz? (c) Calculate the tension required to obtain the proper frequency. (d) Calculate the wavelength of the strings vibration. (e) What is the wavelength of the sound produced in air? (Assume the speed of sound in air is 343 m/s.)

A standing wave is set up in a string of variable length and tension by a vibrator of variable frequency. Both ends of the string are fixed. When the vibrator has a frequency fA, in a string of length LA and under tension TA, nA antinodes are set up in the string. (a) Write an expression for the frequency fA of a standing wave in terms of the number nA, length LA, tension TA, and linear density mA. (b) If the length of the string is doubled to LB 5 2LA, what frequency fB (written as a multiple of fA) will result in the same number of antinodes? Assume the tension and linear density are unchanged. Hint: Make a ratio of expressions for fB and fA. (c) If the frequency and length are held constant, what tension TB will produce nA 1 1 antinodes? (d) If the frequency is tripled and the length of the string is halved, by what factor should the tension be changed so that twice as many antinodes are produced?

A 12.0-kg object hangs in equilibrium from a string with total length of L 5 5.00 m and linear mass density of m 5 0.001 00 kg/m. The string is wrapped around two light, frictionless pulleys that are separated by the distance d 5 2.00 m (Fig. P14.45a). (a) Determine the tension in the string. (b) At what frequency must the string between the pulleys vibrate in order to form the standing-wave pattern shown in Figure P14.45b?

In the arrangement shown in Figure P14.46, an object of mass m 5 5.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L 5 2.0 m. (a) When the vibrator is set to a frequency of 150 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord? (b) How many loops (if any) will result if m is changed to 45 kg? (c) How many loops (if any) will result if m is changed to 10 kg?

A 60.00-cm guitar string under a tension of 50.000 N has a mass per unit length of 0.100 00 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 20 000 Hz?

Standing-wave vibrations are set up in a crystal goblet with four nodes and four antinodes equally spaced around the 20.0-cm circumference of its rim. If transverse waves move around the glass at 900 m/s, an opera singer would have to produce a high harmonic with what frequency in order to shatter the glass with a resonant vibration?

The windpipe of a typical whooping crane is about 5.0 ft. long. What is the lowest resonant frequency of this pipe, assuming it is closed at one end? Assume a temperature of 37C.

The overall length of a piccolo is 32.0 cm. The resonating air column vibrates as in a pipe that is open at both ends. (a) Find the frequency of the lowest note a piccolo can play. (b) Opening holes in the side effectively shortens the length of the resonant column. If the highest note a piccolo can sound is 4 000 Hz, find the distance between adjacent antinodes for this mode of vibration.

The human ear canal is about 2.8 cm long. If it is regarded as a tube that is open at one end and closed at the eardrum, what is the fundamental frequency around which we would expect hearing to be most sensitive?

A tunnel under a river is 2.00 km long. (a) At what frequencies can the air in the tunnel resonate? (b) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.

A pipe open at both ends has a fundamental frequency of 300 Hz when the temperature is 0C. (a) What is the length of the pipe? (b) What is the fundamental frequency at a temperature of 30.0C?

Two adjacent natural frequencies of an organ pipe are found to be 550 Hz and 650 Hz. (a) Calculate the fundamental frequency of the pipe. (b) Is the pipe open at both ends or open at only one end? (c) What is the length of the pipe?

In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide extra loudness. For example, the note at 1.10 3 102 Hz has two strings at this frequency. If one string slips from its normal tension of 6.00 3 102 N to 5.40 3 102 N, what beat frequency is heard when the hammer strikes the two strings simultaneously?

The G string on a violin has a fundamental frequency of 196 Hz. It is 30.0 cm long and has a mass of 0.500 g. While this string is sounding, a nearby violinist effectively shortens the G string on her identical violin (by sliding her finger down the string) until a beat frequency of 2.00 Hz is heard between the two strings. When that occurs, what is the effective length of her string?

Two train whistles have identical frequencies of 1.80 3 102 Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of 2.00 beats/s when the whistles operate together. What are the two possible speeds and directions that the moving train can have?

Two pipes of equal length are each open at one end. Each has a fundamental frequency of 480 Hz at 300 K. In one pipe the air temperature is increased to 305 K. If the two pipes are sounded together, what beat frequency results?

A student holds a tuning fork oscillating at 256 Hz. He walks toward a wall at a constant speed of 1.33 m/s. (a) What beat frequency does he observe between the tuning fork and its echo? (b) How fast must he walk away from the wall to observe a beat frequency of 5.00 Hz?

If a human ear canal can be thought of as resembling an organ pipe, closed at one end, that resonates at a fundamental frequency of 3 000 Hz, what is the length of the canal? Use a normal body temperature of 37C for your determination of the speed of sound in the canal.

Some studies suggest that the upper frequency limit of hearing is determined by the diameter of the eardrum. The wavelength of the sound wave and the diameter of the eardrum are approximately equal at this upper limit. If the relationship holds exactly, what is the diameter of the eardrum of a person capable of hearing 20 000 Hz? (Assume a body temperature of 37.0C.)

A typical sound level for a buzzing mosquito is 40 dB, and that of a vacuum cleaner is approximately 70 dB. Approximately how many buzzing mosquitoes will produce a sound intensity equal to that of a vacuum cleaner?

Assume a 150-W loudspeaker broadcasts sound equally in all directions and produces sound with a level of 103 dB at a distance of 1.60 m from its center. (a) Find its sound power output. If a salesperson claims the speaker is rated at 150 W, he is referring to the maximum electrical power input to the speaker. (b) Find the efficiency of the speaker, that is, the fraction of input power that is converted into useful output power.

Two small loudspeakers emit sound waves of different frequencies equally in all directions. Speaker A has an output of 1.00 mW, and speaker B has an output of 1.50 mW. Determine the sound level (in decibels) at point C in Figure P14.64 assuming (a) only speaker A emits sound, (b) only speaker B emits sound, and (c) both speakers emit sound.

An interstate highway has been built through a neighborhood in a city. In the afternoon, the sound level in an apartment in the neighborhood is 80.0 dB as 100 cars pass outside the window every minute. Late at night, the traffic flow is only five cars per minute. What is the average late-night sound level?

A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. He reports hearing two successive resonances at 52.0 Hz and 60.0 Hz. How deep is the well?

A stereo speaker is placed between two observers who are 36 m apart, along the line connecting them. If one observer records an intensity level of 60 dB, and the other records an intensity level of 80 dB, how far is the speaker from each observer?

Two ships are moving along a line due east (Fig. P14.68). The trailing vessel has a speed relative to a land-based observation point of v1 5 64.0 km/h, and the leading ship has a speed of v2 5 45.0 km/h relative to that point. The two ships are in a region of the ocean where the current is moving uniformly due west at vcurrent 5 10.0 km/h. The trailing ship transmits a sonar signal at a frequency of 1 200.0 Hz through the water. What frequency is monitored by the leading ship?

A quartz watch contains a crystal oscillator in the form of a block of quartz that vibrates by contracting and expanding. Two opposite faces of the block, 7.05 mm apart, are antinodes, moving alternately toward and away from each other. The plane halfway between these two faces is a node of the vibration. The speed of sound in quartz is 3.70 3 103 m/s. Find the frequency of the vibration. An oscillating electric voltage accompanies the mechanical oscillation, so the quartz is described as piezoelectric. An electric circuit feeds in energy to maintain the oscillation and also counts the voltage pulses to keep time.

A flowerpot is knocked off a window ledge from a height d 5 20.0 m above the sidewalk as shown in Figure P14.70. It falls toward an unsuspecting man of height h 5 1.75 m who is standing below. Assume the man below requires 0.300 s to respond to a warning. How close to the sidewalk can the flowerpot fall before it is too late for a warning shouted from the window to reach the man in time?

On a workday, the average decibel level of a busy street is 70 dB, with 100 cars passing a given point every minute. If the number of cars is reduced to 25 every minute on a weekend, what is the decibel level of the street?

A flute is designed so that it plays a frequency of 261.6 Hz, middle C, when all the holes are covered and the temperature is 20.0C. (a) Consider the flute to be a pipe open at both ends and find its length, assuming the middle-C frequency is the fundamental frequency. (b) A second player, nearby in a colder room, also attempts to play middle C on an identical flute. A beat frequency of 3.00 beats/s is heard. What is the temperature of the room?

A block with a speaker bolted to it is connected to a spring having spring constant k 5 20.0 N/m, as shown in Figure P14.73. The total mass of the block and speaker is 5.00 kg, and the amplitude of the units motion is 0.500 m. If the speaker emits sound waves of frequency 440 Hz, determine the (a) lowest and (b) highest frequencies heard by the person to the right of the speaker.

A student stands several meters in front of a smooth reflecting wall, holding a board on which a wire is fixed at each end. The wire, vibrating in its third harmonic, is 75.0 cm long, has a mass of 2.25 g, and is under a tension of 400 N. A second student, moving toward the wall, hears 8.30 beats per second. What is the speed of the student approaching the wall?

By proper excitation, it is possible to produce both longitudinal and transverse waves in a long metal rod. In a particular case, the rod is 150 cm long and 0.200 cm in radius and has a mass of 50.9 g. Youngs modulus for the material is 6.80 3 1010 Pa. Determine the required tension in the rod so that the ratio of the speed of longitudinal waves to the speed of transverse waves is 8.

A 0.500-m-long brass pipe open at both ends has a fundamental frequency of 350 Hz. (a) Determine the temperature of the air in the pipe. (b) If the temperature is increased by 20.0C, what is the new fundamental frequency of the pipe? Be sure to include the effects of temperature on both the speed of sound in air and the length of the pipe.