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physics
mechanics

Physics 5th edition James S. Walker - Solutions

Suppose you would like to double the speed of a wave on a string. By what multiplicative factor must you increase the tension?
A Slinky has a mass of 0.28 kg and negligible length. When it is stretched 1.5 m, it is found that transverse waves travel the length of the Slinky in 0.75 s.(a) What is the force constant, k, of the Slinky?(b) If the Slinky is stretched farther, will the time required for a wave to travel the
OSHA, the Occupational Safety and Health Administration, has established standards for workplace exposure to noise. According to OSHA's Hearing Conservation Standard, the permissible noise exposure per day is 95.0 dB for 4 hours or 105 dB for 1 hour. Assuming the eardrum is 9.5 mm in diameter; find
An organ pipe 3.4 m long is open at one end and closed at the other end. What is the linear distance between a node and the adjacent anti-node for the third harmonic in this pipe?
Two identical strings with the same tension vibrate at 631 Hz. If the tension in one of the strings is increased by 2.25%, what is the resulting beat frequency?
When the plain fin midshipman fish (Porichthys notatus) migrates from deep Pacific waters to the west coast of North America each summer, the males begin to sing their "love song," which some describe as sounding like a low-pitched motorboat. Houseboat residents and shore dwellers are kept awake
A rope of length L and mass M hangs vertically from a ceiling. The tension in the rope is only that due to its own weight.(a) Suppose a wave starts near the bottom of the rope and propagates upward. Does the speed of the wave increase, decrease, or stay the same as it moves up the rope? Explain.(b)
In Problem 59, suppose the observer walks toward one speaker with a speed of 1.35 m/s.(a) What frequency does the observer hear from each speaker?.(b) What beat frequency does the observer hear?(c) How far must the observer walk to go from one point of constructive interference to the next?(d) How
Suppose the air passages in a certain P. walkeri crest produce a bent tube 2.7 m long. What is the fundamental frequency of this tube, assuming the bend has no effect on the frequency? (For comparison, a typical human hearing range is 20 Hz to 20 kHz.)A. 0.0039 HzB. 32 HzC. 64 HzD. 130 Hz
Paleontologists believe the crest of a female P. walkeri was probably shorter than the crest of a male. If this was the case, would the fundamental frequency of a female be greater than, less than, or equal to the fundamental frequency of a male?
Suppose the fundamental frequency of a particular female was 74 Hz. What was the length of the air passages in this female's crest?A. 1.2 mB. 2.3 mC. 2.7 mD. 4.6 m
Two strings are made of the same material and have equal tensions. String 1 is thick; string 2 is thin.(a) Is the speed of waves on string 1 greater than, less than, or equal to the speed of waves on string 2?(b) Choose the best explanation from among the following:I. Since the strings are made of
As a young P. walkeri matured, the air passages in its crest might increase in length from 1.5 m to 2.7 m, causing a decrease in the standing wave frequencies. Referring to Figure 14-54, do you expect the change in the fundamental frequency to be greater than, less than, or equal to the change in
Suppose the engineer adjusts the speed of the train until the sound he hears reflected from the cliff is 775 Hz. The train's whistle still produces a tone of 650.0 Hz.(a) Is the new speed of the train greater than, less than, or equal to 21.2 m/s? Explain.(b) Find the new speed of the train.
Suppose the train is backing away from the cliff with a speed of 18.5 m/s and is sounding its 650.0-Hz whistle.(a) What is the frequency heard by the observer standing near the tunnel entrance?(b) What is the frequency heard by the engineer?
Suppose we add more water to the soda pop bottle.(a) Does the fundamental frequency increase, decrease, or stay the same? Explain.(b) Find the fundamental frequency if the height of water in the bottle is increased to 7.5 cm. The height of the bottle is still 26.0 cm.
The speed of sound increases slightly with temperature.(a) Does the fundamental frequency of the bottle increase, decrease, or stay the same as the air heats up on a warm day? Explain.(b) Find the fundamental frequency if the speed of sound in air increases to 348 m/s. Assume the bottle is 26.0 cm
Two strings are made of the same material and have waves of equal speed. String 1 is thick; string 2 is thin.(a) Is the tension in string 1 greater than, less than, or equal to the tension in string 2?(b) Choose the best explanation from among the following:I. String 1 must have a greater tension
The three waves, A, B and C, shown in FIGURE 14-43 propagate on strings with equal tensions and equal mass per length. Rank the waves in order of increasing(a) Frequency,(b) Wavelength, and(c) Speed. Indicate ties where appropriate.In figure 14-43
A brother and sister try to communicate with a string tied between two tin cans (FIGURE 14-44). If the string is 7.6 m long, has a mass of 29 g, and is pulled taut with a tension of 18 N, how much time does it take for a wave to travel from one end of the string to the other?In figure 14-44
(a) Suppose the tension is increased in the previous problem. Does a wave take more, less, or the same time to travel from one end to the other? Calculate the time of travel for tensions of(b) 22 N(c) 32 N.In figure 14-44
A 5.7-m wire with a mass of 81 g is attached to the mast of a sailboat. If the wire is given a "thunk" at one end, it takes 0.084 s for the resulting wave to reach the other end.(a) What is the tension in the wire?(b) Would the tension found in part (a) be larger or smaller if the mass of the wire
A 4.5-m-long rope of mass 1.8 kg hangs from a ceiling.(a) What is the tension in the rope at the bottom end?(b) What is the wave speed in the rope at the bottom end?(c) What is the tension in the rope at the top end, where it is attached to the ceiling?(d) What is the wave speed in the rope at the
Two steel guitar strings have the same length. String A has a diameter of 0.50 mm and is under 410.0 N of tension. String B has a diameter of 1.0 mm and is under a tension of 820.0 N. Find the ratio of the wave speeds, vA/vB, in these two strings.
Use dimensional analysis to show how the speed v of a wave on a string of circular cross section depends on the tension in the string, F, the radius of the string, R, and its mass per volume, ρ.
A surfer floating beyond the breakers notes 17 waves per minute passing her position. If the wavelength of these waves is 38 m, what is their speed?
Write an expression for a harmonic wave with an amplitude of 0.19 m, a wavelength of 2.6 m, and a period of 1.2 s. The wave is transverse, travels to the right, and has a displacement of 0.19 m at t = 0 and x = 0.
Write an expression for a transverse harmonic wave that has a wavelength of 2.6 m and propagates to the right with a speed of 14.3 m/s. The amplitude of the wave is 0.11 m, and its displacement at t = 0 and x = 0 is 0.11 m.
The vertical displacement of a wave on a string is described by the equation y(x, t) = A sin1Bx - Ct), in which A, B, and C are positive constants.(a) Does this wave propagate in the positive or negative x direction?(b) What is the wavelength of this wave?(c) What is the frequency of this wave?(d)
As it travels through a crystal, a light wave is described by the function E(x,t) = A cos [(1.54 × 107)x - (2.98 × 1015)t]. In this expression, x is measured in meters and t is measured in seconds. What is the speed of the light wave?
A wave on a string is described by the following equation:(a) What is the amplitude of this wave?(b) What is its wavelength?(c) What is its period?(d) What is its speed?(e) In which direction does the wave travel?
Consider a harmonic wave with the following wave functions:Sketch this wave from x = 0 to x = 9.0 cm for the following times:(a) t = 0;(b) t = 4.0 s;(c) t = 8.0 s.(d) What is the least amount of time required for a given point on this wave to move from y = 0 to y = 12 cm?
Four waves are described by the following equations, in which all distances are measured in centimeters and all times are measured in seconds:yA = 10 cos(3x - 4t)yB = 10 cos(5x + 4t)yC = 20 cos(-10x + 60t)yD = 20 cos(-4x - 20t)(a) Which of these waves travel in the +x direction?(b) Which of these
At Zion National Park a loud shout produces an echo 1.55 s later from a colorful sandstone cliff. How far away is the cliff?
Dolphins of the open ocean are classified as Type II Odontocetes (toothed whales). These animals use ultrasonic "clicks" with a frequency of about 55 kHz to navigate and find prey.(a) Suppose a dolphin sends out a series of clicks that are reflected back from the bottom of the ocean 75 m below. How
The lowest note on a piano is A, four octaves below the A given in Table 14-3. The highest note on a piano is C, four octaves above middle C. Find the frequencies and wavelengths (in air) of these notes.
The speed of surface waves in water decreases as the water becomes shallower. Suppose waves travel across the surface of a lake with a speed of 2.0 m/s and a wavelength of 1.5 m. When these waves move into a shallower part of the lake, their speed decreases to 1.6 m/s, though their frequency
A meteor that explodes in the atmosphere creates infrasound waves that can travel multiple times around the globe. On February 15, 2013, the Chelyabinsk meteor produced infrasound waves with a wavelength of 6.4 km that propagated 8840 km in 8.53 h. What was the frequency of these waves?
A sound wave in air has a frequency of 405 Hz.(a) What is its wavelength?(b) If the frequency of the sound is increased, does its wavelength increase, decrease, or stay the same? Explain.(c) Calculate the wavelength for a sound wave with a frequency of 485 Hz.
When you drop a rock into a well, you hear the splash 1.5 seconds later.(a) How deep is the well?(b) If the depth of the well were doubled, would the time required to hear the splash be greater than, less than, or equal to 3.0 seconds? Explain.
A rock is thrown downward into a well that is 7.62 m deep. If the splash is heard 1.17 seconds later, what was the initial speed of the rock?
If the distance to a point source of sound is doubled, by what multiplicative factor does the intensity change?
The intensity level of sound in a truck is 88 dB. What is the intensity of this sound?
The distance to a point source is decreased by a factor of three.(a) By what multiplicative factor does the intensity increase?(b) By what additive amount does the intensity level increase?
Sound 1 has an intensity of 48.0 W/m2. Sound 2 has an intensity level that is 3.5 dB greater than the intensity level of sound 1. What is the intensity of sound 2?
A bird-watcher is hoping to add the white-throated sparrow to her "life list" of species. How far could she be from the bird described in Example 14-8 and still be able to hear it? Assume no reflections or absorption of the sparrow's sound.
Residents of Hawaii are warned of the approach of a tsunami by sirens mounted on the tops of towers. Suppose a siren produces a sound that has an intensity level of 120 dB at a distance of 2.0 m. Treating the siren as a point source of sound, and ignoring reflections and absorption, find the
A tsunami traveling across deep water can have a speed of 750 km/h and a wavelength of 310 km. What is the frequency of such a wave?
In a pig-calling contest, a caller produces a sound with an intensity level of 107 dB. How many such callers would be required to reach the pain level of 120 dB?
Twenty violins playing simultaneously with the same intensity combine to give an intensity level of 82.5 dB.(a) What is the intensity level of each violin?(b) If the number of violins is increased to 40, will the combined intensity level be more than, less than, or equal to 165 dB? Explain.
The radius of a typical human eardrum is about 4.0 mm. Find the energy per second received by an eardrum when it listens to sound that is(a) At the threshold of hearing and(b) At the threshold of pain.
A horn produces sound with frequency ƒ0. Let the frequency you hear when you are at rest and the horn moves toward you with a speed u be ƒ1; let the frequency you hear when the horn is at rest and you move toward it with a speed u be ƒ2.(a) Is ƒ1 greater than, less than, or equal to ƒ2?(b)
You are heading toward an island in your speedboat when you see a friend standing on shore at the base of a cliff. You sound the boat's horn to get your friend's attention. Let the wavelength of the sound produced by the horn be λ1, the wavelength as heard by your friend be λ2, and the wavelength
When the bell in a clock tower rings with a sound of 475 Hz, a pigeon roosting in the belfry flies directly away from the bell. If the pigeon hears a frequency of 448 Hz, what is its speed?
A car approaches a train station with a speed of 24 m/s. A stationary train at the station sounds its 166-Hz horn. What frequency is heard by the driver of the car?
A bat moving with a speed of 3.25 m/s and emitting sound of 35.0 kHz approaches a moth at rest on a tree trunk.(a) What frequency is heard by the moth?(b) If the speed of the bat is increased, is the frequency heard by the moth higher or lower?(c) Calculate the frequency heard by the moth when the
A motorcycle and a police car are moving toward one another. The police car emits sound with a frequency of 523 Hz and has a speed of 32.2 m/s. The motorcycle has a speed of 14.8 m/s. What frequency does the motorcyclist hear?
Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 460 Hz; as the truck recedes, you hear a tone of 410 Hz. How much time will it take for the truck to get from your position to the fire 5.0 km away, assuming
A stationary boat bobs up and down with a period of 2.3 s when it encounters the waves from a moving boat.(a) What is the frequency of the waves?(b) If the crests of the waves are 8.5 m apart, what is their speed?
For a science experiment, you would like to use the Doppler effect to double the perceived frequency of a harmonica, from the 261.7-Hz tone (middle C) that it emits, to 523.3 Hz (C5 note).(a) Which strategy will accomplish your goal more easily: move the harmonica, or move the observer?(b)
Two bicycles approach one another, each traveling with a speed of 8.50 m/s.(a) If bicyclist A beeps a 315-Hz horn, what frequency is heard by bicyclist B?(b) Which of the following would cause the greater increase in the frequency heard by bicyclist B: (i) bicyclist A speeds up by 1.50 m/s, or (ii)
A train on one track moves in the same direction as a second train on the adjacent track. The first train, which is ahead of the second train and moves with a speed of 36.8 m/s, blows a horn whose frequency is 124 Hz. If the frequency heard on the second train is 135 Hz, what is its speed?
Two cars traveling with the same speed move directly away from one another. One car sounds a horn whose frequency is 422 Hz and a person in the other car hears a frequency of 385 Hz. What is the speed of the cars?
The Shinkansen, the Japanese "bullet" train, runs at high speed from Tokyo to Nagoya. Riding on the Shinkansen, you notice that the frequency of a crossing signal changes markedly as you pass the crossing. As you approach the crossing, the frequency you hear is ƒ; as you recede from the crossing
Pulses A, B, C, and D all travel at 10 m>s on the same string but in opposite directions. The string is depicted at time t = 0 in FIGURE 14-45. The small pulses have an amplitude of 2.0 cm, and the large pulses have an amplitude of 4.0 cm. Find the displacement of point P at times(a) t = 0.10 s(b)
Pulses A, B, C, and D all travel at 10 m>s on the same string but in opposite directions. The string is depicted at time t = 0 in FIGURE 14-46. The small pulses have an amplitude of 2.0 cm, and the large pulse has an amplitude of 4.0 cm. Find the displacement of point P at times(a) t = 0.10 s(b) t
A pair of in-phase stereo speakers is placed side by side, 0.914 m apart. You stand directly in front of one of the speakers, 2.44 m from the speaker. What is the lowest frequency that will produce constructive interference at your location?
Two violinists, one directly behind the other, play for a listener directly in front of them. Both violinists sound concert A 1440 Hz2.(a) What is the smallest separation between the violinists that will produce destructive interference for the listener?(b) Does this smallest separation increase or
Two loudspeakers are placed at either end of a gymnasium, both pointing toward the center of the gym and equidistant from it. The speakers emit 266-Hz sound that is in phase. An observer at the center of the gym experiences constructive interference. How far toward either speaker must the observer
A 4.5-Hz wave with an amplitude of 12 cm and a wavelength of 27 cm travels along a stretched horizontal string.(a) How far does a given peak on the wave travel in a time interval of 0.50 s?(b) How far does a knot on the string travel in the same time interval?(c) How would your answers to parts (a)
Two speakers with opposite phase are positioned 3.5 m apart, both pointing toward a wall 5.0 m in front of them (FIGURE 14-47). An observer standing against the wall midway between the speakers hears destructive interference. If the observer hears constructive interference after moving 0.84 m to
Suppose, in Example 14-13 that the speakers have opposite phase. What is the lowest frequency that gives destructive interference in this case?
When you blow across the opening of a partially filled 2-L soda pop bottle you hear a tone.(a) If you take a sip of the pop and blow across the opening again, does the tone you hear have a higher frequency, a lower frequency, or the same frequency as before?(b) Choose the best explanation from
An organ pipe that is open at both ends is 3.5 m long. What is its fundamental frequency?
A string 2.5 m long with a mass of 3.6 g is stretched between two fixed points with a tension of 91 N. Find the frequency of the fundamental on this string.
The unique sound of a person's voice arises from the frequencies of the standing waves that occur in a person's chest, trachea, larynx, mouth, nose, and sinuses. Suppose a person's voice has a strong resonant frequency at 890 Hz when she is breathing air. What will be the frequency of the same
The fundamental wavelength for standing sound waves in an empty pop bottle is 0.88 m.(a) What is the length of the bottle?(b) What is the frequency of the third harmonic of this bottle?
A string is tied down at both ends. Some of the standing waves on this string have the following frequencies: 100 Hz, 200 Hz, 250 Hz, and 300 Hz. It is also known that there are no standing waves with frequencies between 250 Hz and 300 Hz.(a) What is the fundamental frequency of this string?(b)
The human ear canal is much like an organ pipe that is closed at one end (at the tympanic membrane or eardrum) and open at the other (FIGURE 14-48). A typical ear canal has a length of about 2.4 cm.(a) What are the fundamental frequency and wavelength of the ear canal?(b) Find the frequency and
A guitar string 66 cm long vibrates with a standing wave that has three antinodes.(a) Which harmonic is this?(b) What is the wavelength of this wave?
The speed of a deepwater wave with a wavelength l is given approximately by v = √gλ/2π. Find (a) The speed(b) The frequency of a deepwater wave with a wavelength of 4.5 m.
A guitar string has a mass per length of 2.33 × 10−3 kg/m and a fundamental frequency of 146.8 Hz when it is under a tension of 82.4 N. The string breaks, and its owner has only a spare string of mass per length 6.79 × 10−3 kg/m. (a) In order to use the new string to play the same note,
A 0.323-kg clothesline is stretched with a tension of 53.4 N between two poles 6.10 m apart. What is the frequency of (a) The fundamental and (b) The second harmonic? (c) If the tension in the clothesline is increased, do the frequencies in parts (a) and (b) increase, decrease, or stay the same?
The organ pipe in FIGURE 14-49 is 2.75 m long.(a) What is the frequency of the standing wave shown in the pipe?(b) What is the fundamental frequency of this pipe?
The frequency of the standing wave shown in FIGURE 14-50 is 185 Hz.(a) What is the fundamental frequency of this pipe?(b) What is the length of the pipe?
An organ pipe open at both ends has a harmonic with a frequency of 440 Hz. The next higher harmonic in the pipe has a frequency of 495 Hz. Find (a) The frequency of the fundamental and (b) The length of the pipe.
When guitar strings A and B are plucked at the same time, a beat frequency of 2 Hz is heard. If string A is tightened, the beat frequency increases to 3 Hz. Which of the two strings had the lower frequency initially?
(a) Is the beat frequency produced when a 245-Hz tone and a 240-Hz tone are played together greater than, less than, or equal to the beat frequency produced when a 140-Hz tone and a 145-Hz tone are played together? (b) Choose the best explanation from among the following: I. The beat frequency is
You have three tuning forks with frequencies of 252 Hz, 256 Hz, and 259 Hz. What beat frequencies are possible with these tuning forks?
To tune middle C on a piano, a tuner hits the key and at the same time sounds a 261-Hz tuning fork. If the tuner hears 3 beats per second, what are the possible frequencies of the piano key?
Two musicians are comparing their clarinets. The first clarinet produces a tone that is known to be 466 Hz. When the two clarinets play together they produce eight beats every 3.00 seconds. If the second clarinet produces a higher pitched tone than the first clarinet, what is the second clarinet's
In shallow water of depth d the speed of waves is approximately v = √gd. Find(a) The speed(b) The period of a wave with a wavelength of 2.6 cm in water that is 0.75 cm deep.
Two strings that are fixed at each end are identical, except that one is 0.560 cm longer than the other. Waves on these strings propagate with a speed of 34.2 m/s, and the fundamental frequency of the shorter string is 212 Hz. (a) What beat frequency is produced if each string is vibrating with
Identical cellos are being tested. One is producing a fundamental frequency of 120.9 Hz on a string that is 1.25 m long and has a mass of 109 g. On the second cello an identical string is fingered to reduce the length that can vibrate. If the beat frequency produced by these two strings is 5.25 Hz,
A friend in another city tells you that she has two organ pipes of different lengths, one open at both ends, the other open at one end only. In addition, she has determined that the beat frequency caused by the second-lowest frequency of each pipe is equal to the beat frequency caused by the
Figure 14-51 shows a wave on a string moving to the right. For each of the points indicated on the string, A-F, state whether it is (I, moving upward; II, moving downward; or III, instantaneously at rest) at the instant pictured.
The fundamental of an organ pipe that is closed at one end and open at the other end is 261.6 Hz (middle C). The second harmonic of an organ pipe that is open at both ends has the same frequency. What are the lengths of these two pipes?
The loudest sound produced by a living organism on Earth is made by the bowhead whale (Balaena mysticetus). These whales can produce a sound that, if heard in air at a distance of 3.00 m, would have an intensity level of 127 dB. This is roughly the equivalent of 5000 trumpeting elephants. How far
Physicist Robert Adair, once appointed the "official physicist to the National League" by the commissioner of baseball, believes that the "crack of the bat" can tell an outfielder how well the ball has been hit. According to Adair, a good hit makes a sound of 510 Hz, while a poor hit produces a
A standing wave of 603 Hz is produced on a string that is 1.33 m long and fixed on both ends. If the speed of waves on this string is 402 m/s, how many antinodes are there in the standing wave?

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