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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

P and S waves from an earthquake travel at different speeds, and this difference helps in locating the earth quake “epicenter” (where the disturbance took place)(a) Assuming typical speeds of 8.5
An earthquake-produced surface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies),
What is the ratios of? (a) The intensities, and (b) The amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10km and 20km from the source.
The intensity of an earthquake wave passing through the Earth is measured to be 2.0 X 106 J/m2 s at a distance of 48 km from the source.(a) What was its intensity when it passed a point only 1.0km
Two earthquake waves of the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two waves?
Two waves traveling along a stretched string have the same frequency, but one transports three times the power of the other. What is the ratio of the amplitudes of the two waves?
A bug on the surface of a pond is observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5cm, by what
The two pulses shown in Fig. 11-52 are moving toward each other.(a) Sketch the shape of the string at the moment they directly overlap.(b) Sketch the shape of the string a few moments later.(c) In
If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?
A violin string vibrates at 294 Hz when un-fingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is only two-thirds of the string vibrates as a
A particular string resonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which i will resonate.
The velocity of waves on a string is 92m/s. If the frequency of standing waves is 475 Hz, how far apart are two adjacent nodes?
If two successive overtones of a vibrating string are 280Hz and 350 Hz, what is the frequency of the fundamental?
A guitar string is 90 cm long and has a mass of 3.6g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. What are the frequencies of the
A particular guitar string is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?
Once end of a horizontal string is attached to a small-amplitude mechanical 60-Hz vibrator the string€™s mass per unit length is 3.9 X 10-4 kg/m. The string passes over a pulley, a distance
In Problem 59, the length of the string may be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L
When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to
An earthquake P wave traveling at 8.0 km/s strikes a boundary within the Earth between two kinds of material. If it approaches the boundary at an incident angle of 47o and the angle of refraction is
Water waves approach an underwater “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s. If the incident wave crests make a 34o angle with the shelf, what will be the angle of refraction?
A sound wave is traveling in warm air when it hits a layer of cold, dense air. If the sound wave hits the cold air interface at an angle of 25o, what is the angle of refraction? Assume that the cold
A longitudinal earthquake wave strikes a boundary between two types of rock at a 38o angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8 assuming that
A satellite dish is about 0.5m in diameter. According to the user’s manual, the dish has to be pointed in the direction of the satellite, but an error of about 2o is allowed without loss of
A tsunami of wavelength 250 km and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much
An energy-absorbing car bumper has a spring stiffness constant of 550 kN/m. Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2m/s
A 65-kg person jumps from a window to a fire net 18m below, which stretches the net 1.1m. Assume that the net behaves like a simple spring, and (a) Calculate how much it would stretch if the same
A mass m is gently placed on the end of a freely hanging spring. The mass then falls 33cm before it stops and begins to rise. What is the frequency of the oscillation?
A 950-kg car strikes a huge spring at a speed of 22m/s (Fig. 11-54), compressing the spring 5.0 m.(a) What is the spring stiffness constant of the spring?(b) How long is the car in contact with the
When you walk with a cup of coffee (diameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11-55).
The ripples in a certain groove 10.8cm from the center of a 33-rpm phonograph record have a wavelength of 1.70mm. What will be the frequency of the sound emitted?
A 2.00-kg mass vibrates according to the equation x = 0.650 cos 7.40t, where x is in meters and t in seconds. Determine (a) The amplitude, (b) The frequency(c) The total energy, and (d) The kinetic
A simple pendulum oscillates with frequency f. What is its frequency if it accelerates at 0.50g?(a) Upward, and (b) Downward?
A 220-kg wooden raft floats on a lake. When a 75-kg man stands on the raft, it sinks 4.0cm deeper into the water. When the steps off, the raft vibrates for a while. (a) What is the frequency of
Two strings on a musical instrument are tuned to play at 392 Hz (G) and 440 Hz (A).(a) What are the frequencies of the first two overtones for each string?(b) If the two strings have the same length
Consider a sine wave traveling down the stretched two-part cord of Fig. 11-33. Determine a formula (a) For the ratio of the speeds of the wave in the heavy section versus that in the lighter section,
A tuning fork vibrates at a frequency of 264Hz, and the tip of each prong moves 1.8mm to either side of center. Calculate(a) The maximum speed and (b) The maximum acceleration of the tip of a prong.
A diving board oscillates with simple harmonic motion of frequency 1.5 cycles per sound. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there
A string can have a €œfree€ end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11-57). Determine the wavelengths of the resonant
A “seconds” pendulum has a period of exactly 2.000 s—each one-way swing takes 1.000s.(a) What is the length of a second pendulum in Austin, Texas, where g = 9.793 m/s2?(b) If the pendulum is
A mass hanging from a spring can oscillate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical
A block with mass M = 5.0kg rests on a frictionless table and is attached by a horizontal spring (k = 130 N/m) to a wall. A second block, of mass m = 1.25 kg, rests on top of M. The coefficient of
A 10.0 m-long wire of mass 123 g is stretched under a tension of 255N. A pulse is generated at one end, and 20.0ms later a second pulse is generated at the opposite end. Where will the two pulses
A block of mass M is suspended from a ceiling by a spring with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will
A crane has hoisted a 1200-kg car at the junkyard. The steel crane cable is 22m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the
A block of Jello rests on a plate as shown in Fig. 11-58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The Jello springs back and begins to
What is the evidence that sound travels as a wave?
What is the evidence that sound is form of energy?
Children sometimes play with a homemade €œtelephone€ by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the
When a sound wave passes from air into water, do you expect the frequency or wavelength to change?
What evidence can you give that the speed of sound in air does not depend significantly on frequency?
The voice of a person who has inhaled helium sounds very high-pitched. Why?
How will the air temperature in a room affect the pitch of organ pipes?
Explain how a tube might be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car muffler).
Why are the frets on a guitar (Fig. 12-30) spaced closer together as you move up the fingerboard toward the bridge?
A noisy truck approaches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter”—you hear more of the
A noisy truck approaches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter”—you hear more of the
In Fig 12-16, if the frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together?
Traditional methods of protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new
Consider the two waves shown in Fig. 12-31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies of two sound waves with slightly different
Is there a Doppler shift if the source and observer move in the same direction, with the same velocity? Explain.
If a wind is blowing, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed?
Figure 12-32 shows various positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position a through E, will the child hear the
A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0s after shouting. Estimate the length of the lake.
A sailor strikes the side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5s later. How deep is the ocean at this point? Assume
(a) Calculate the wavelengths in air at 20oC for sounds 20,000 Hz. (b) What is the wavelength of a 10-MHz ultra-sonic wave?
An ocean fishing boat is drifting just above a school of tuna on a foggy day. Without warning, an engine back-fire occurs on another boat 1.0 km away (Fig. 12-33). How much time elapses before the
A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 3.5s later. How high is the cliff?
A person, with his ear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and
Calculate the percent error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30oC(b) 10oC
What is the intensity of a sound at the pain level of 120 dB? Compare it to that of a whisper at 20dB.
What is the sound level of a sound whose intensity is 2.0 X 10-6 W/m2?
If two firecrackers produce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded?
A person standing a certain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the
A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device?
(a) Estimate the power output of sound from a person speaking in normal conversation. Use Table 12-2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. (b) How many
A 50-dB sound wave strikes an eardrum whose area is 50 X 10-5 m2.(a) How much energy is absorbed by the eardrum per sound?(b) At this rate, how long would it take your eardrum to receive a total
Expensive amplifier A is rated at 250 W, while the more modest amplifier B is rated at 40W.(a) Estimate the sound level in decibels you would expect at a point 3.5m from a loudspeaker connected in
At a rock concert, a dB meter registered 130 dB when placed 2.8m in front of a loudspeaker on the stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the
Human beings can typically detect a difference in sound level of 2.0 dB. What is the tario of the amplitudes of two sounds whose levels differ by this amount?
If the amplitude of a sound wave is tripled, (a) By what factor will the intensity increase?(b) By how many dB will the sound level increase?
Two sound waves have equal displacement amplitudes, but one has twice the frequency of the other. What is the 4ratio of their intensities?
What would be the sound level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13mm at 300 Hz?
A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12-6)
What are the lowest and highest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12-6).
Your auditory system can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at? (a) 100 Hz, (b) 5000 Hz (See Fig. 12-6)
The string on a violin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32cm, and it has a mass of 0.35g. Under what tension the string must be placed?
An organ pipe it 112 cm long. What are the fundamental and first three audible overtones if the pipe is?(a) Closed at one end, and(b) Open at both ends?
(a) What resonant frequency would you expect from blowing across the top of an empty soda bottle that is 18cm deep, if you assumed it was a closed tube? (b) How would that change if it was one-third
If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required?
A tight guitar string has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original length?
An un-fingered guitar string is 0.73m long and is tuned to play E above middle C (330 Hz).(a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440
(a) Determine the length of an open organ pipe that emits middle C (262 Hz) when the temperature is 21oC. (b) What are the wavelength and frequency of the fundamental standing wave in the tube?(c)
An organ is in tune at 20oC. By what percent will the frequency be off at 5.0oC?
How far from the mouthpiece of the flute in Example 12-10 should the hole be that must be uncovered to play D above middle C at 294 Hz?
(a) At T = 20oC, how long must an open organ pipe be to have a fundamental frequency of 294 Hz? (b) If this pipe if filled with helium, what is its fundamental frequency?
A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency
A uniform narrow tube 1.80m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is? (a) The fundamental frequency, and(b) The speed of sound in
A pipe in air at 20oC is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?
How many overtones are present within the audible range for a 2.14-m-long organ pipe at 20oC (a) If it is open, and(b) It is closed?
The human ear canal is approximately 2.5cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the

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