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physics
oscillations mechanical waves

Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

A man strikes one end of a thin rod with a hammer. The speed of sound in the rod is 15 times the speed of sound in air. A woman, at the other end with her ear close to the rod, hears the sound of the blow twice with a 0.12 s interval between; one sound comes through the rod and the other comes
Diagnostic ultrasound of frequency 4.50 MHz is used to examine tumors in soft tissue. (a) What is the wavelength in air of such a sound wave? (b) If the speed of sound in tissue is 1500 m/s, what is the wavelength of this wave in tissue?
The pressure in a traveling sound wave is given by the equation Δp = (1.50 Pa) sin π[(0.900 m-1) x - (315 s-1)t]. Find the (a) Pressure amplitude, (b) Frequency, (c) Wavelength, and (d) Speed of the wave.
If the form of a sound wave traveling through air is s(x, t) = (6.0 nm) cos (kx + (3000 rad/s)t + Φ), how much time does any given air molecule along the path take to move between displacements s = + t2.0 nm and s = – 2.0 nm?
Underwater illusion one clue used by your brain to determine the direction of a source of sound is the time delay ?t between the arrival of the sound at the ear closer to the source and the arrival at the farther ear. Assume that the source is distant so that a wave front from it is approximately
A handclap on stage in an amphitheater sends out sound waves that scatter from terraces of width w = 0.75 m (Figure). The sound returns to the stage as a periodic series of pulses, one from each terrace; the parade of pulses sounds like a played note.(a) Assuming that all the rays in Figure are
Figure shows the output from a pressure monitor mounted at a point along the path taken by a sound wave of a single frequency traveling at 343 m/s through air with a uniform density of 1.21 kg/m3. The vertical axis scale is set by Δps = 4.0mPa. If the displacement function of the wave is written
A sound wave of the form s = sm cos (kx – wt + Φ) travels at 343 m/s through air in a long horizontal tube. At one instant, air molecule A at x = 2.000 m is at its maximum positive displacement of 6.00 nm and air molecule B at x = 2.070 m is at a positive displacement of 2.00 nm. All the
Two sound waves, from two different sources with the same frequency, 540Hz, travel in the same direction at 330 m/s. The sources are in phase. What is the phase difference of the waves at a point that is 4.40 m from one source and 4.00m from the other?
Figure shows two isotropic point sources of sound, S1 and S2. The sources emit waves in phase at wavelength 0.50 m; they are separated by D = 1.75 m. If we move a sound detector along a large circle centered at the midpoint between the sources, at how many points do waves arrive at the detector(a)
In Figure sound with a 40.0 cm wavelength travels rightward from a source and through a tube that consists of a straight portion and a half-circle. Part of the sound wave travels through the half-circle and then rejoins the rest of the wave, which goes directly through the straight portion. This
In Figure two speakers separated by distance dt = 2.00 m are in phase. Assume the amplitudes of the sound waves from the speakers are approximately the same at the listener's ear at distance d2 = 3.75 m directly in front of one speaker. Consider the full audible range for normal hearing, 20 Hz to
In Figure sound waves A and B, both of wavelength λ, are initially in phase and traveling rightward, as indicated by the two rays. Wave A is reflected from four surfaces but ends up traveling in its original direction. Wave B ends in that direction after reflecting from two surfaces. Let distance
Two loudspeakers are located 3.35 m apart on an outdoor stage. A listener is 18.3 m from one and I9.5 m from the other. During the sound check, a signal generator drives the two speakers in phase with the same amplitude and frequency. The transmitted frequency is swept through the audible range (20
Figure shows four isotropic point sources of sound that are uniformly spaced on an x axis. The sources emit sound at the same wavelength λ and same amplitude sm, and they emit in phase. A point P is shown on the x axis. Assume that as the sound waves travel to P, the decrease in their amplitude is
Figure shows two point sources S1 and S2, that emit sound of wavelength λ = 2.00m. The emissions are isotropic and in phase, and the separation between the sources is d = 16.0 m. At any point P on the x axis, the wave from S1 and the wave from S2 interfere. When P is very far away (x ?? ??), what
A 1.0 W point source emits sound waves isotropically. Assuming that the energy of the waves is conserved, find the intensity(a) 1.0 m from the source and(b) 2.5 m from the source
A source emits sound waves isotropically. The intensity of the waves 2.50 m from the source is 1.91 x 10–4 W/m2. Assuming that the energy of the waves is conserved, find the power of the source.
Two sounds differ in sound level by 1.00 dB. What is the ratio of the greater intensity to the smaller intensity?
A sound wave of frequency 300 Hz has an intensity of 1.00μW/m2. What is the amplitude of the air oscillations caused by this wave?
The source of a sound wave has a power of 1.00μW. If it is a point source,(a) What is the intensity 3.00 m away and(b) What is the sound level in decibels at that distance?
A certain sound source is increased in sound level by 30.0 dB. By what multiple is(a) Its intensity increased and(b) Its pressure amplitude increased?
Suppose that the sound level of a conversation is initially at an angry 70 dB and then drops to a soothing 50 dB. Assuming that the frequency of the sound is 500 Hz, determine the(a) Initial and(b) Final sound intensities and the(c) Initial and(d) Final sound wave amplitudes.
Male Rana catesbeiana bullfrogs are known for their loud mating call. The call is emitted not by the frog's mouth but by its eardrums, which lie on the surface of the head. And, surprisingly, the sound has nothing to do with the frog's inflated throat. If the emitted sound has a frequency of 260 Hz
Approximately a third of people with normal hearing have ears that continuously emit a low-intensity sounded outward through the ear canal. A person with such spontaneous otoacoustic emission is rarely aware of the sound, except perhaps in a noise-free environment, but occasionally the emission is
When you "crack" a knuckle, you suddenly widen the knuckle cavity, allowing more volume for the synovial fluid inside it and causing a gas bubble suddenly to appear in the fluid. The sudden production of the bubble, called "cavitations," produces a sound pulse-the cracking sound. Assume that the
Party hearing as the number of people at a party increases you must raise your voice for a listener to hear you against the background noise of the other partygoers. However, once you reach the level of yelling, the only way you can be heard is if you move closer to your listener, into the
A point source emits 30.0 W of sound isotropically. A small microphone intercepts the sound in an area of 0.750 cm2, 200 m from the source. Calculate (a) The sound intensity there and (b) The power intercepted by the microphone.
Two atmospheric sound sources A and B emit isotropically at constant power. The sound levels F of their emissions are plotted in Figure versus the radial distance r from the sources. The vertical axis scale is set by β1 = 85.0 dB and β1 = 65.0 dB. What are? (a) The ratio of the larger power to
A sound source sends a sinusoidal sound wave of angular frequency 3000rad/s and amplitude 12.0nm through a tube of air. The internal radius of the tube is 2.00 cm.(a) What is the average rate at which energy (the sum of the kinetic and potential energies) is transported to the opposite end of the
The crest of a Parasaurolophus dinosaur skull contains a nasal passage in the shape of a long, bent tube open at both ends. The dinosaur may have used the passage to produce sound by setting up the fundamental mode in it.(a) If the nasal passage in a certain Parasaurolophus fossil is 2.0 m long,
A violin string 15.0 cm long and fixed at both ends oscillates in its n = 1 mode. The speed of waves on the string is 250 m/s, and the speed of sound in air in 348 m/s. What are the(a) Frequency and (b) Wavelength of the emitted sound wave?
A sound wave in a fluid medium is reflected at a barrier so that a standing wave is formed. The distance between nodes is 3.8cm, and the speed of propagation is 1500 m/s. Find the frequency of the sound wave.
In pipe A, the ratio of a particular harmonic frequency to the next lower harmonic frequency is 1.2. In pipe B, the ratio of a particular harmonic frequency to the next lower harmonic frequency is 1.4. How many open ends ate in?(a) Pipe A and (b) Pip e B?
Organ pipe A, with both ends open, has a fundamental frequency of 300 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. How long are (a) Pipe A and (b) Pipe B?
(a) Find the speed of waves on a violin string of mass 800 mg and length 22.0 cm if the fundamental frequency is 920 Hz. (b) What is the tension in the string? For the fundamental, what is the wavelength of (c) The waves on the string and (d) The sound waves emitted by the string?
The water level in a vertical glass tube 1.00 m long can be adjusted to any position in the tube. A tuning fork vibrating at 686 Hz is held just over the open top end of the tube, to set up a standing wave of sound in the air-filled top portion of the tube. (That air-filled top portion acts as a
In Figure S is a small loudspeaker driven by an audio oscillator with a frequency that is varied from 1000 Hz to 2000 Hz, and D is a cylindrical pipe with two open ends and a length of 45.7 cm. The speed of sound in the air-filled pipe is 344 m/s.(a) At how many frequencies does the sound from the
One of the harmonic frequencies of tube A with two open ends ts 325 Hz. The next-highest harmonic frequency is 390 Hz. (a) What harmonic frequency is next highest after the harmonic frequency 195 Hz? (b) What is the number of this next-highest harmonic? One of the harmonic frequencies of tube B
A violin string 30.0 cm long with linear density 0.650 g/m is placed near a loudspeaker that is fed by an audio oscillator of variable frequency. It is found that the string is set into oscillation only at the frequencies 880 and 1320 Hz as the frequency of the oscillator is varied over the range
A tube 1.20 m long is closed at one end. A stretched wire is placed near the open end. The wire is 0.330 m long and has a mass of 9.60 g. It is fixed at both ends and oscillates in its fundamental mode. By resonance, it sets the air column in the tube into oscillation at that column's fundamental
A well with vertical sides and water at the bottom resonates at 7 .00 Hz and at no lower frequency. (The air-filled portion of the well acts as a tube with one closed end and one open end.) The air in the well has a density of 1.10 kg/m3 and a bulk modulus of 1.33 x 105 Pa. How far down in the well
Pipe A, which is 1.20 m long and open at both ends, oscillates at its third lowest harmonic frequency, it is filled with air for which the speed of sound is 343 m/s. Pipe B, which is closed at one end, oscillates at its second lowest harmonic frequency. This frequency of B happens to match the
The A string of a violin is a little too tightly stretched. Beats at 4.00 per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at concert A (440Ht). What is the period of the violin string oscillation?
A tuning fork of unknown frequency makes 3.00 beats per second with a standard fork of frequency 384 Hz. The beat frequency decreases when a small piece of wax is put on a prong of the first fork. What is the frequency of this fork?
Two identical piano wires have a fundamental frequency of 600 Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 6.0beats/s when both wires oscillate simultaneously?
You have five tuning forks that oscillate at close but different frequencies. What are the (a) Maximum and (b) Minimum number of different beat frequencies you can produce by sounding the forks two at a time, depending on how the frequencies differ?
A state trooper chases a speeder along a straight road; both vehicles move at 160 km/h. The siren on the trooper's vehicle produces sound at a frequency of 500 Hz. What is the Doppler shift in the frequency heard by the speeder?
An ambulance with a siren emitting a whine at 1,600 Hz overtakes and passes a cyclist pedaling a bike at 2.44 m/s. After being passed, the cyclist hears a frequency of 1590 Hz. How fast is the ambulance moving?
A whistle of frequency 540 Hz moves in a circle of radius 60.0 cm at an angular speed of 15.0 rad/s. What are the(a) Lowest and(b) Highest frequencies heard by a listener a long distance away, at rest with respect to the center of the circle?
A stationary motion detector sends sound waves of frequency 0.1.50 MHz toward a truck approaching at a speed of 45.0 m/s. What is the frequency of the waves reflected back to the detector?
An acoustic burglar alarm consists of a source emitting waves of frequency 28.0 kHz. What is the beat frequency between the source waves and the waves reflected from an intruder walking at an average speed of 0.950 m/s directly away from the alarm?
A sound source A and a reflecting surface B move directly toward each other. Relative to the air, the speed of source A is 29.9 m/s, the speed of surface B is 65.8 m/s, and the speed of sound is 329 m/s. The source emits waves at frequency 1200 Hz as measured in the source frame. In the reflector
In Figure a French submarine and a U.S. submarine move toward each other during maneuvers in motionless water in the North Atlantic. The French sub moves at speed vF = 50.00 km/h, and the U.S. sub at vUS = 70.00 km/h. The French sub sends out a sonar signal (sound wave in water) at 1.000 x 103 Hz.
A stationary detector measures the frequency of a sound source that first moves at constant velocity directly toward the detector and then (after passing the detector) directly away from it. The emitted frequency is f. During the approach the detected frequency is f’app and during the recession
A bat is flitting about in a cave, navigating via ultrasonic bleeps. Assume that the sound emission frequency of the bat is 39 000 Hz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.025 times the speed of sound in air. What frequency does the bat hear reflected
Figure shows four tubes with lengths 1.0 m or 2.0 m, with one or two open ends as drawn. The third harmonic is set up in each tube, and some of the sound that escapes from them is detected by detector D, which moves directly away from the tubes. In terms of the speed of sound v, what speed must the
A girl is sitting near the open window of a train that is moving at a velocity of 10.00 m/s to the east. The girl's uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at frequency 500.0 Hz. The air is still.(a) What frequency does the uncle hear?(b)
Two trains are traveling toward each other at 30.5 m/s relative to the ground. One train is blowing a whistle at 500 Hz.(a) What frequency is heard on the other train in still air?(b) What frequency is heard on the other train if the wind is blowing at 30.5 m/s toward the whistle and away from the
A 2000 Hz siren and a civil defense official are both at rest with respect to the ground. What frequency does the official hear if the wind is blowing at 12m/s?(a) From source to official and(b) From official to source?
The shock wave off the cockpit of the FA 18 in Figure has an angle of about 60o. The airplane was traveling at about 1350 km/h when the photograph was taken. Approximately what was the speed of sound at the airplane's altitude?
A jet plane passes over you at a height of 5000 m and a speed of Mach 1.5.(a) Find the Mach cone angle (the sound speed is 33L m/s).(b) How long after the jet passes directly overhead does the shock wave reach you?
A plane flies at 1.25 times the speed of sound. Its sonic boom reaches a man on the ground 1.00 min after the plane passes directly overhead. What is the altitude of the plane assume the speed of sound to be 330 m/s.
In Figure sound of wavelength 0.850 m is emitted isotropically by point source S. Sound ray I extends directly to detector D, at distance L = 10.0 m. Sound ray 2 extends to D via a reflection (effectively, a "bouncing") of the sound at a flat surface. That reflection occurs on a perpendicular
A detector initially moves at constant velocity directly toward a stationary sound source and then (after passing it) directly from it. The emitted frequency is f. During the approach the detected frequency is f’app and during the recession it is f’rec. If the frequencies are related by
Two sound waves with an amplitude of 12 nm and a wavelength of 35 cm travel in the same direction through a long tube, with a phase difference of π/3 rad. What are the(a) Amplitude and(b) Wavelength of the net sound wave produced by their interference? If, instead, the sound waves travel through
A sinusoidal sound wave moves at 343 m/s through air in the positive direction of an x axis. At one instant, air molecule A is at its maximum displacement in the negative direction of the axis while air molecule B is at its equilibrium position. The separation between those molecules is 15.0cm, and
In Figure sound waves A and B, both of wavelength λ, are initially in phase and traveling rightward, as indicated by the two rays. Wave A is reflected from four surfaces but ends up traveling in its original direction. What multiple of wavelength λ is the smallest value of distance L in the
A trumpet player on a moving railroad flatcar moves toward a second trumpet player standing alongside the track while both play a 440 Hz note. The sound waves heard by a stationary observer between the two players have a beat frequency of 4.0beats/s. What is the flatcar's speed?
A siren emitting a sound of frequency 1000 Hz moves away from you toward the face of a cliff at a speed of 10 m/s. Take the speed of sound in air as 330 m/s.(a) What is the frequency of the sound you hear coming directly from the siren?(b) What is the frequency of the sound you hear reflected off
A sound source moves along an x axis, between detectors A and B. The wavelength of the sound detected at A is 0.500 that of the sound detected at B. What is the ratio vs/v of the speed of the source to the speed of sound?
A certain loudspeaker system emits sound isotropically with a frequency of 2000 Hz and an intensity of 0.960mW/m2 at a distance of 6.10 m. Assume that there are no reflections.(a) What is the intensity at 30.0 m? At 6.10 m, what are?(b) The displacement amplitude and(c) The pressure amplitude?
At a certain point, two waves produce pressure variations given by Δp1 = Δpm sin wt and Δp2 = Δpm sin (wt – Φ). At this point, what is the ratio Δpr/Δpm where Δpr, is the pressure amplitude of the resultant wave, if d is(a) 0,(b) π/2,(c) π/3, and(d) π/4?
The sound intensity is 0.0080 W/m2 at a distance of 10 m from an isotropic point source of sound.(a) What is the power of the source?(b) What is the sound intensity 5.0 m from the source?(c) What is the sound level L0 m from the source?
The average density of Earth's crust 10 km beneath the continents is 2.7 g/cm3. The speed of longitudinal seismic waves at that depth, found by timing their arrival from distant earthquakes, is 5.4 km/s. Use this information to find the bulk modulus of Earth's crust at that depth. For comparison,
Two identical tuning forks can oscillate at 440Hz. A person is located somewhere on the line between them. Calculate the beat frequency as measured by this individual if(a) She is standing still and the tuning forks move in the same direction along the line at 3.00 m/s, and(b) The tuning forks are
You can estimate your distance from a lightning stroke by counting the seconds between the flash you see and the thunder you later hear. By what integer should you divide the number of seconds to get the distance in kilometers?
(a) If two sound waves, one in air and one in (fresh) water are equal in intensity and angular frequency, what is the ratio of the pressure amplitude of the wave in water to that of the wave in air? Assume the water and the air are at 20oC. (See Table)(b) If the pressure amplitudes are equal
Find the ratios (greater to smaller) of the(a) Intensities,(b) Pressure amplitudes, and(c) Particle displacement amplitudes for two sounds whose sound levels differ by 37 dB.
Figure shows an air-filled, acoustic interferometer, used to demonstrate the interference of sound waves. Sound source S is an oscillating diaphragm; D is a sound detector, such as the ear or a microphone. Path SBD can be varied in length, but path SAD is fixed. At D, the sound wave coming along
A bullet is fired with a speed of 685 m/s. Find the angle made by the shock cone with the line of motion of the bullet.
A sperm whale (Figure a) vocalizes by producing a series of clicks. Actually, the whale makes only a single sound near the front of its head to start the series. Part of that sound then emerges from the head into the water to become the first click of the series. The rest of the sound travels
A continuous sinusoidal longitudinal wave is sent along a very long coiled spring from an attached oscillating source. The wave travels in the negative direction of an x axis; the source frequency is 25 Hz; at any instant the distance between successive points of maximum expansion in the spring is
At a distance of 10 km, a 100 Hz horn assumed to be an isotropic point source is barely audible. At what distance would it begin to cause pain.
At a distance of 10 km, a 100 Hz horn, assumed to be an isotropic point source, is barely audible. At what distance would it begin to cause pain?
A pipe 0.60 m long and closed at one end is filled with an unknown gas. The third lowest harmonic frequency for the pipe is 750 Hz.(a) What is the speed of sound in the unknown gas?(b) What is the fundamental frequency for this pipe when it is filled with the unknown gas?
Four sound waves are to be sent through the same tube of air, in the same direction: What is the amplitude of the resultant wave?
Straight line AB connects two point sources that are 5.00 m apart, emit 300 Hz sound waves of the same amplitude, and emit exactly out of phase.(a) What is the shortest distance between the midpoint of AB and a point on AB where the interfering waves cause maximum oscillation of the air molecules?
A point source that is stationary on an x axis emits a sinusoidal sound wave at a frequency of 686 Hz and speed 343 m/s. The wave travels radially outward from the source, causing air molecules to oscillate radially inward and outward. Let us define a wave front as a line that connects points where
You are standing at a distance D from an isotropic point source of sound. You walk 50.0 m toward the source and observe that the intensity of the sound has doubled. Calculate the distance D.
On July 10, 1996, a granite block broke away from a wall in Yosemite Valley and, as it began to slide down the wall, was launched into projectile motion. Seismic waves produced by its impact with the ground triggered seismographs as far away as 200 km. Later measurements indicated that the block
An avalanche of sand along some rare desert sand dunes can produce a booming that is loud enough to be heard l0 km away. The booming apparently results from a periodic oscillation of the sliding layer of sand-the layer's thickness expands and contracts. If the emitted frequency is 90 Hz, what
Passengers in an auto traveling at 16.0 m/s toward the east hear a siren frequency of 950 Hz from an emergency vehicle approaching them from behind at a speed (relative to the air and ground) of 40.0 m/s. The speed of sound in air is 340 m/s.(a) What siren frequency does a passenger riding in the
Ultrasound, which consists of sound waves with frequencies above the human audible range, can be used to produce an image of the interior of a human body. Moreover, ultrasound can be used to measure the speed of the blood in the body; it does so by comparing the frequency of the ultrasound sent
Pipe A has only one open end; pipe B is four times as long and has two open ends. Of the lowest 10 harmonic numbers hp of pipe B, what are the(a) Smallest,(b) Second smallest, and(c) Third smallest values at which a harmonic frequency of B matches one of the harmonic frequencies of A?
Water fall acoustics the turbulent impact of the water in a waterfall causes the surrounding ground to oscillate in a wide range of low frequencies. If the water falls freely (instead of hitting rock on the way down), the oscillations are greatest in amplitude at a particular frequency fm. This
A person a railroad car blows a trumpet note at 440Hz. The car is moving toward a wall at20.0 m/s. Calculate the frequency of(a) The sound as received at the wall and(b) The reflected sound arriving back at the trumpeter.
A police car is chasing a speeding Porsche 911. Assume that the Porsche's maximum speed is 80.0m/s and the police car's is 54.0 m/s. At the moment both cars reach their maximum speed, what frequency will the Porsche driver hear if the frequency of the police car's siren is 440 Hz? Take the speed of
A sound wave travels out uniformly in all directions from a point source.(a) Justify the following expression for the displacement s of the transmitting medium at any distance r from the source: s = b/r sin k (r – vt), where b is a constant. Consider the speed, direction or propagation,
In Figure S1 and S2 are two isotropic point sources of sound. They emit waves in phase at wavelength 0.50 m; they are separated by D = 1.60 m. If we move a sound detector along a large circle centered at the midpoint between the sources, at how many points do waves arrive at the detector(a) Exactly

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