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physics
mechanics

Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

A transverse wave on a string is described byy(x, t) = (1.2 cm) sin [(0.50p rad/s)t − (1.00p rad/m)x]Find the maximum velocity and the maximum acceleration of a point on the string. Plot graphs for displacement y versus t, velocity vy versus t, and acceleration (y versus t at x = 0.
What is the wavelength of the radio waves transmitted by an FM station at 90 MHz? (Radio waves travel at 3.0 ( 10 8 m/s.)
(a) What is the speed of propagation of the pulse shown in the figure? (b) At what average speed does the point at x = 2.0 m move during this time interval?
A longitudinal wave has a wavelength of 10 cm and an amplitude of 5.0 cm and travels in the y -direction. The wave speed in this medium is 80 cm/s. (a) Describe the motion of a particle in the medium as the wave travels through the medium. (b) How would your answer differ if the wave were
An underground explosion sends out both transverse (S waves) and longitudinal (P waves) mechanical wave pulses (seismic waves) through the crust of the Earth. Suppose the speed of transverse waves is 8.0 km/s and that of longitudinal waves is 10.0 km/s. On one occasion, both waves follow the same
The graph shows ground vibrations recorded by a seismograph 180 km from the focus of a small earthquake. It took the waves 30.0 s to travel from their source to the seismograph. Estimate the wavelength.
When the string of a guitar is pressed against a fret, the shortened string vibrates at a frequency 5.95% higher than when the previous fret is pressed. If the length of the part of the string that is free to vibrate is 64.8 cm, how far from one end of the string are the first three frets located?
A guitar string has a fundamental frequency of 300.0 Hz.(a) What are the next three lowest standing wave frequencies?(b) If you press a finger lightly against the string at its midpoint so that both sides of the string can still vibrate, you create a node at the midpoint. What are the lowest four
A sign is hanging from a single metal wire, as shown in part(a) of the drawing. The shop owner notices that the wire vibrates at a fundamental resonance frequency of 660 Hz, which irritates his customers. In an attempt to fix the problem, the shop owner cuts the wire in half and hangs the sign from
(a) Write an equation for a surface seismic wave moving along the −x-axis with amplitude 2.0 cm, period 4.0 s, and wavelength 4.0 km. Assume the wave is harmonic, x is measured in m, and t is measured in s. (b) What is the maximum speed of the ground as the wave moves by? (c) What is the wave
The formula for the speed of transverse waves on a spring is the same as for a string. (a) A spring is stretched to a length much greater than its relaxed length. Explain why the tension in the spring is approximately proportional to the length. (b) A wave takes 4.00 s to travel from one end of
Deep-water waves are dispersive (their wave speed depends on the wavelength). The restoring force is provided by gravity. Using dimensional analysis, find out how the speed of deep-water waves depends on wavelength l, assuming that l and g are the only relevant quantities. (Mass density does not
In contrast to deep-water waves, shallow ripples on the surface of a pond are due to surface tension. The surface tension ( of water characterizes the restoring force; the mass density ( of water characterizes the water's inertia. Use dimensional analysis to determine whether the surface waves are
(a) What is the position of the peak of the pulse shown in the figure with Problem 6 at t = 3.00 s? (a) What is the speed of propagation of the pulse shown in the figure? (b) At what average speed does the point at x = 2.0 m move during this time interval?(b) When does the peak of the pulse arrive
A seismic wave is described by the equation y(x, t) = (7.00 cm) cos [(6.00( rad/cm) x + (20.0( rad/s)t] The wave travels through a uniform medium in the x -direction. (a) Is this wave moving right ( + x-direction) or left (−x-direction)? (b) How far from their equilibrium positions do the
The drawing shows a snapshot of a transverse wave moving to the left on a string. The wave speed is 10.0 m/s. At the instant the snapshot is taken, (a) in what direction is point A moving? (b) In what direction is point B moving? (c) At which of these points is the speed of the string segment (not
Consider a point just to the left of point A in the drawing with Problem 71. Plot the position of that point and the velocity of that point as a function of time as the wave passes the point.
Two speakers spaced a distance 1.5 m apart emit coherent sound waves at a frequency of 680 Hz in all directions. The waves start out in phase with each other. A listener walks in a circle of radius greater than one meter centered on the midpoint of the two speakers. At how many points does the
(a) Use a graphing calculator or computer graphing program to plot y versus x for the function y(x, t) = (5.0 cm) [sin (kx − (t) + sin (kx + (t)] For the times t = 0, 1.0 s, and 2.0 s. Use the values k = (/ (5.0 cm) and ( = ((/ 6.0) rad/s. (b) Is this a traveling wave? If not, what kind of wave
Show that the amplitudes of the graphs you made in Problem 74 satisfy the equation A′ = 2 A cos (( t), where A′ is the amplitude of the wave you plotted and A is 5.0 cm, the amplitude of the waves that were added together.
The pulse of Problems 37-38 travels on a string that has fixed ends.1. The pulse travels on a string whose ends at x = 0 and x = 4.0 m are both fixed in place. Sketch the shape of the string at t = 2.2 s.2. The pulse travels on a string whose ends at x = 0 and x = 4.0 m are both fixed in place.
When the tension in a cord is 75 N, the wave speed is 140 m/s. What is the linear mass density of the cord?
A metal guitar string has a linear mass density of m = 3.20 g/m. What is the speed of transverse waves on this string when its tension is 90.0 N?
Explain why the pitch of a bassoon is more sensitive to a change in air temperature than the pitch of a cello. (That's why wind players keep blowing air through the instrument to keep it in tune.)
A moving source emits a sound wave that is heard by a moving observer. Imagine a thin wall at rest between the source and observer. The wall completely absorbs the sound and instantaneously emits an identical sound wave. Use this scenario to explain why we can combine the Doppler shifts due to
Explain why the displacement of air elements at condensations and rarefactions is zero.
Why is the speed of sound in solids generally much faster than the speed of sound in air?
The source and observer of a sound wave are both at rest with respect to the ground. The wind blows in the direction from source to observer. Is the observed frequency Doppler-shifted? Explain.
Many brass instruments have valves that increase the total length of the pipe from mouthpiece to bell. When a valve is depressed, is the fundamental frequency raised or lowered? What happens to the pitch?
When the viola section of an orchestra with six members plays together, is the sound 6 times as loud as when a single viola plays? Explain. Is the intensity 6 times what it would be for a single viola? [The six sound waves are not coherent.]
The fundamental frequency of the highest note on the piano is 4.186 kHz. Most musical instruments do not go that high; only a few singers can produce sounds with fundamental frequencies higher than around 1 kHz. Yet a good-quality stereo system must reproduce frequencies up to at least 16 to 18
On a warm day, a piano is tuned to match an organ in an auditorium. Will the piano still be in tune with the organ the next morning, when the room is cold? If not, will the organ be higher or lower in pitch than the piano? (Assume that the piano's tuning doesn't change. Why is that a reasonable
Many real estate agents have an ultrasonic rangefinder that enables them to quickly and easily measure the dimensions of a room. The device is held to one wall and reads the distance to the opposite wall. How does it work?
For high-frequency sounds, the ear's principal method of localization is the difference in intensity sensed by the two ears. Why can't the ear reliably use this method for low-frequency sounds? Doesn't the head cast a "sound shadow" regardless of the frequency? Explain. [Consider diffraction of
For low-frequency sounds, the ear uses the phase difference between the sound waves arriving at the two ears to determine direction. Why can't the ear reliably use phase difference for high-frequency sounds? Explain.
A sign along the road in Tompkins County reads, "State Law: Noise Limit, 90 decibels." If you were subjected to such a noise level for an extended period of time, would you need to worry about your hearing being affected?
Why is it that your own voice sounds strange to you when you hear it played back on a tape recorder, but your friends all agree that it is just what your voice sounds like?[ Consider the media through which the sound wave travels when you usually hear your own voice.]
What is the purpose of the gel that is spread over the skin before an ultrasonic imaging procedure? [The speed of sound in the gel is similar to the speed in the body, while the speed in air is much slower. What happens to a wave at an abrupt change in wave speed?]
A stereo system whose amplifier can produce 60 W per channel is replaced by one rated 120 W per channel. Would you expect the new stereo to be able to play twice as loudly as the old one? Explain.
Bats emit ultrasonic waves with a frequency as high as 1.0 ( 10 5 Hz. What is the wavelength of such a wave in air of temperature 15°C?
Stan and Ollie are standing next to a train track. Stan puts his ear to the steel track to hear the train coming. He hears the sound of the train whistle through the track 2.1 s before Ollie hears it through the air. How far away is the train?
A sound wave with an intensity level of 80.0 dB is incident on an eardrum of area 0.600 × 10−4 m2. How much energy is absorbed by the eardrum in 3.0 min?
The sound level 25 m from a loudspeaker is 71 dB. What is the rate at which sound energy is produced by the loudspeaker, assuming it to be an isotropic source?
In a factory, three machines produce noise with intensity levels of 85 dB, 90 dB, and 93 dB. When all three are running, what is the intensity level? How does this compare to running just the loudest machine?
At the race track, one race car starts its engine with a resulting intensity level of 98.0 dB at point P. Then seven more cars start their engines. If the other seven cars each produce the same intensity level at point P as the first car, what is the new intensity level with all eight cars running?
(a) What is the pressure amplitude of a sound wave with an intensity level of 120.0 dB in air? (b) What force does this exert on an eardrum of area 0.550 × 10−4 m2?
An intensity level change of + 1.00 dB corresponds to what percentage change in intensity?
(a) Show that if I2 = 10.0 I1, then (2 = (1 + 10.0 dB. (A factor of 10 increase in intensity corresponds to a 10.0 dB increase in intensity level.) (b) Show that if I2 = 2.0 I1, then (2 = (1 + 3.0 dB. (A factor of 2 increase in intensity corresponds to a 3.0-dB increase in intensity level.
At a rock concert, the engineer decides that the music isn't loud enough. He turns up the amplifiers so that the amplitude of the sound, where you're sitting, increases by 50.0%. (a) By what percentage does the intensity increase? (b) How does the intensity level (in dB) change?
Humans can hear sounds with frequencies up to about 20.0 kHz, but dogs can hear frequencies up to about 40.0 kHz. Dog whistles are made to emit sounds that dogs can hear but humans cannot. If the part of a dog whistle that actually produces the high frequency is made of a tube open at both ends,
Dolphins emit ultrasonic waves with a frequency as high as 2.5 × 105 Hz. What is the wavelength of such a wave in seawater at 25°C?
(a) What should be the length of an organ pipe, closed at one end, if the fundamental frequency is to be 261.5 Hz?(b) What is the fundamental frequency of the organ pipe of part (a) if the temperature drops to 0.0 ° C?
Repeat Problem 20 for an organ pipe that is open at both ends.(a) What should be the length of an organ pipe, closed at one end, if the fundamental frequency is to be 261.5 Hz?(b) What is the fundamental frequency of the organ pipe of part (a) if the temperature drops to 0.0°C?
An organ pipe that is open at both ends has a fundamental frequency of 382 Hz at 0.0°C. What is the fundamental frequency for this pipe at 20.0°C?
What is the length of the organ pipe in Problem 22?An organ pipe that is open at both ends has a fundamental frequency of 382 Hz at 0.0°C. What is the fundamental frequency for this pipe at 20.0°C?
A certain pipe has resonant frequencies of 234 Hz, 390 Hz, and 546 Hz, with no other resonant frequencies between these values. (a) Is this a pipe open at both ends or closed at one end? (b) What is the fundamental frequency of this pipe? (c) How long is this pipe?
In an experiment to measure the speed of sound in air, standing waves are set up in a narrow pipe open at both ends using a speaker driven at 702 Hz. The length of the pipe is 2.0 m. What is the air temperature inside the pipe (assumed reasonably near room temperature, 20°C to 35°C)? [The
When a tuning fork is held over the open end of a very thin tube, as in Fig. 12.7, the smallest value of L that produces resonance is found to be 30.0 cm.(a) What is the wavelength of the sound? [Assume that the displacement antinode is at the open end of the tube.](b) What is the next larger value
Two tuning forks, A and B, excite the next-to-lowest resonant frequency in two air columns of the same length, but A's column is closed at one end and B's column is open at both ends. What is the ratio of A's frequency to B's frequency?
How long a pipe is needed to make a tuba whose lowest note is low C (frequency 130.8 Hz)? Assume that a tuba is a long straight pipe open at both ends.
An aluminum rod, 1.0 m long, is held lightly in the middle. One end is struck head-on with a rubber mallet so that a longitudinal pulse-a sound wave-travels down the rod. The fundamental frequency of the longitudinal vibration is 2.55 kHz. (a) Describe the location of the node(s) and antinode(s)
At a baseball game, a spectator is 60.0 m away from the batter. How long does it take the sound of the bat connecting with the ball to travel to the spectator's ears? The air temperature is 27.0°C.
A violin is tuned by adjusting the tension in the strings. Brian's A string is tuned to a slightly lower frequency than Jennifer's, which is correctly tuned to 440.0 Hz. (a) What is the frequency of Brian's string if beats of 2.0 Hz are heard when the two bow the strings together? (b) Does Brian
A piano tuner sounds two strings simultaneously. One has been previously tuned to vibrate at 293.0 Hz. The tuner hears 3.0 beats per second. The tuner increases the tension on the as-yet untuned string, and now when they are played together the beat frequency is 1.0 s−1. (a) What was the original
An auditorium has organ pipes at the front and at the rear of the hall. Two identical pipes, one at the front and one at the back, have fundamental frequencies of 264.0 Hz at 20.0°C. During a performance, the organ pipes at the back of the hall are at 25.0°C, while those at the front are still at
A musician plays a string on a guitar that has a fundamental frequency of 330.0 Hz. The string is 65.5 cm long and has a mass of 0.300 g.(a) What is the tension in the string?(b) At what speed do the waves travel on the string?(c) While the guitar string is still being plucked, another musician
A cello string has a fundamental frequency of 65.40 Hz. What beat frequency is heard when this cello string is bowed at the same time as a violin string with frequency of 196.0 Hz? [The beats occur between the third harmonic of the cello string and the fundamental of the violin.]
An ambulance traveling at 44 m/s approaches a car heading in the same direction at a speed of 28 m/s. The ambulance driver has a siren sounding at 550 Hz. At what frequency does the driver of the car hear the siren?
At a factory, a noon whistle is sounding with a frequency of 500 Hz. As a car traveling at 85 km/h approaches the factory, the driver hears the whistle at frequency (i. After driving past the factory, the driver hears frequency (f. What is the change in frequency (f − (i heard by the driver?
In parts of the midwestern United States, sirens sound when a severe storm that may produce a tornado is approaching. Mandy is walking at a speed of 1.56 m/s directly toward one siren and directly away from another siren when they both begin to sound with a frequency of 698 Hz. What beat frequency
A source of sound waves of frequency 1.0 kHz is traveling through the air at 0.50 times the speed of sound. (a) Find the frequency of the sound received by a stationary observer if the source moves toward her. (b) Repeat if the source moves away from her instead.
A source of sound waves of frequency 1.0 kHz is stationary. An observer is traveling at 0.50 times the speed of sound. (a) What is the observed frequency if the observer moves toward the source? (b) Repeat if the observer moves away from the source instead.
A lightning flash is seen in the sky and 8.2 s later the boom of the thunder is heard. The temperature of the air is 12°C. (a) What is the speed of sound at that temperature? [Light is an electromagnetic wave that travels at a speed of 3.00 × 108 m/s.] (b) How far away is the lightning strike?
A child swinging on a swing set hears the sound of a whistle that is being blown directly in front of her. At the bottom of her swing when she is moving toward the whistle, she hears a higher pitch, and at the bottom of her swing when she is moving away from the swing she hears a lower pitch. The
A source and an observer are each traveling at 0.50 times the speed of sound. The source emits sound waves at 1.0 kHz. Find the observed frequency if (a) the source and observer are moving toward each other; (b) the source and observer are moving away from each other; (c) the source and observer
Blood flow rates can be found by measuring the Doppler shift in frequency of ultrasound reflected by red blood cells (known as angiodynography). If the speed of the red blood cells is v, the speed of sound in blood is u, the ultrasound source emits waves of frequency f, and we assume that the blood
Show that for a moving source, the fractional shift in observed frequency is equal to vs / v, the source's speed as a fraction of the speed of sound. [Use the binomial approximation from Appendix A.5.]
The pitch of the sound from a race car engine drops the musical interval of a fourth when it passes the spectators. This means the frequency of the sound after passing is 0.75 times what it was before. How fast is the race car moving?
A ship is lost in a dense fog in a Norwegian fjord that is 1.80 km wide. The air temperature is 5.0°C. The captain fires a pistol and hears the first echo after 4.0 s. (a) How far from one side of the fjord is the ship? (b) How long after the first echo does the captain hear the second echo?
A ship mapping the depth of the ocean emits a sound of 38 kHz. The sound travels to the ocean floor and returns 0.68 s later. (a) How deep is the water at that location? (b) What is the wavelength of the wave in water? (c) What is the wavelength of the reflected wave as it travels into the air,
A boat is using sonar to detect the bottom of a freshwater lake. If the echo from a sonar signal is heard 0.540 s after it is emitted, how deep is the lake? Assume the temperature of the lake is uniform and at 25 ° C.
A geological survey ship mapping the floor of the ocean sends sound pulses down from the surface and measures the time taken for the echo to return. How deep is the ocean at a point where the echo time (down and back) is 7.07 s? The temperature of the seawater is 25 ° C.
A bat emits chirping sounds of frequency 82.0 kHz while hunting for moths to eat. If the bat is flying toward the moth at a speed of 4.40 m/s and the moth is flying away from the bat at 1.20 m/s, what is the frequency of the sound wave reflected from the moth as observed by the bat? Assume it is a
During a thunderstorm, you can easily estimate your distance from a lightning strike. Count the number of seconds that elapse from when you see the flash of lightning to when you hear the thunder. The rule of thumb is that 5 s elapse for each mile of distance. Verify that this rule of thumb is
The bat of Problem 49 emits a chirp that lasts for 2.0 ms and then is silent while it listens for the echo. If the beginning of the echo returns just after the outgoing chirp is finished, how close to the moth is the bat? Is the change in distance between the two significant during a 2.0-ms time
Doppler ultrasound is used to measure the speed of blood flow Problem 42.In problem 42 Blood flow rates can be found by measuring the Doppler shift in frequency of ultrasound reflected by red blood cells (known as angiodynography). If the speed of the red blood cells is v, the speed of sound in
(a) In Problem 42, find the beat frequency between the outgoing and reflected sound waves.In problem 42,Blood flow rates can be found by measuring the Doppler shift in frequency of ultrasound reflected by red blood cells (known as angiodynography). If the speed of the red blood cells is v, the
A 30.0-cm-long string has a mass of 0.230 g and is vibrating at its next-to-lowest natural frequency (2. The tension in the string is 7.00 N.(a) What is (2?(b) What are the frequency and wavelength of the sound in the surrounding air if the speed of sound is 350 m/s?
Kyle is climbing a sailboat mast and is 5.00 m above the surface of the ocean, while his friend Rob is scuba diving below the boat. Kyle shouts to someone on another boat and Rob hears him shout 0.0210 s later. The ocean temperature is 25°C and the air is at 20°C. How deep is Rob below the boat?
What are the four lowest standing wave frequencies for an organ pipe that is 4.80 m long and closed at one end?
The length of the auditory canal in humans averages about 2.5 cm. What are the lowest three standing wave frequencies for a pipe of this length open at one end? What effect might resonance have on the sensitivity of the ear at various frequencies? (Refer to Fig. 12.12. Frequencies critical to
Some bats determine their distance to an object by detecting the difference in intensity between echoes. (a) If intensity falls off at a rate that is inversely proportional to the distance squared, show that the echo intensity is inversely proportional to the fourth power of distance? (b) The bat
The Vespertilionidae family of bats detect the distance to an object by timing how long it takes for an emitted signal to reflect off the object and return. Typically they emit sound pulses 3 ms long and 70 ms apart while cruising. (a) If an echo is heard 60 ms later (v sound = 331 m/s), how far
At what frequency f does a sound wave in air have a wavelength of 15 cm, about half the diameter of the human head? Some methods of localization work well only for frequencies below f, while others work well only above f. (See Conceptual Questions 4 and 5.)
A copper alloy has a Young's modulus of 1.1 × 1011 Pa and a density of 8.92 ( 103 kg/m3. What is the speed of sound in a thin rod made from this alloy? Compare your result with that given in Table 12.1.
Horseshoe bats use the Doppler effect to determine their location. A Horseshoe bat flies toward a wall at a speed of 15 m/s while emitting a sound of frequency 35 kHz. What is the beat frequency between the emission frequency and the echo?
According to a treasure map, a treasure lies at a depth of 40.0 fathoms on the ocean floor due east from the lighthouse. The treasure hunters use sonar to find where the depth is 40.0 fathoms as they head east from the lighthouse. What is the elapsed time between an emitted pulse and the return of
When playing fortissimo (very loudly), a trumpet emits sound energy at a rate of 0.800 W out of a bell (opening) of diameter 12.7 cm. (a) What is the sound intensity level right in front of the trumpet? (b) If the trumpet radiates sound waves uniformly in all directions, what is the sound intensity
One cold and windy winter day, Zach notices a humming sound coming from his chimney when the chimney is open at the top and closed at the bottom. He opens the chimney at the bottom and notices that the sound changes. He goes over to the piano to try to match the chimney is producing with the bottom
A periodic wave is composed of the superposition of three sine waves whose frequencies are 36, 60, and 84 Hz. The speed of the wave is 180 m/s. What is the wavelength of the wave? The 36 Hz is not necessarily the fundamental frequency.

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