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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

Singing in the Shower. A pipe closed at both ends can have standing waves inside of it, but you normally don't hear them because little of the sound can get out. But you can hear them if you are
You blow across the open mouth of an empty test tube and produce the fundamental standing wave of the air column inside the rest tube. The speed of sound in air is 344 m/s and the test tube acts as a
You have a stopped pipe of adjustable length close to a taut 85.0-cm, 7.25-g wire under a tension of 4110 N. You want to adjust the length of the pipe so that, when it produces sound at its
Two loudspeakers, A and B (Fig. 16.40), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the
Two loudspeakers, A and B (Fig. 16.40), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. The frequency of the sound waves produced
Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 12.0 m to the right of speaker A. The frequency of the waves emitted by each speaker is
Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 172 Hz. You are 8.00 m from A. What is the
Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 860 Hz. Point P is 12.0 m from A and 13.4 m from
Two guitarists attempt to play the same note of wavelength 6.50 cm at the same time, but one of the instruments is slightly out of tune and plays a note of wavelength 6.52 cm instead. What is the
Two organ pipes open at one end but closed at the other, are each 1.14 m long. One is now lengthened by 2.00 cm. Find the frequency of the beat they produce when playing together in their fundamental.
Two identical taut strings under the same tension F produce a note of the same fundamental frequency fo• The tension in one of them is now increased by a very small amount ΔF. (a) If they are
On the planet Arrakis a male omithoid is flying toward his mate at 25.0 m/s while singing at a frequency of 1200 Hz. If the stationary female hears a tone of 1240 Hz, what is the speed of sound in
In Example 16.19 (Section 16.8), suppose the police car is moving away from the warehouse at 20 m/s. What frequency does the driver of the police car hear reflected from the warehouse?
Two train whistles, A and B, each have a frequency of 392 Hz. A is stationary and B is moving toward the right (away from A) at a speed of35.0 m/s. A listener is between the two whistles and is
A railroad train is traveling at 25.0 m/s in still air. The frequency of the note emitted by the locomotive whistle is 400 Hz. What is the wavelength of the sound waves? (a) In front of the
A swimming duck paddles the water with its feet once every 1.6 s, producing surface waves with this period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.32
Moving Source vs. Moving Listener. (a) A sound source producing 1.00-kHz waves moves toward a stationary listener at one-half the speed of sound. What frequency will the listener hear? (b) Suppose
A car alarm is emitting sound waves of frequency 520 Hz. You are on a motorcycle, traveling directly away from the car. How fast must you be traveling if you detect a frequency of 490 Hz?
A railroad train is traveling at 30.0 m/s in still air. The frequency of the note emitted by the train whistle is 262 Hz. What frequency is heard by a passenger on a train moving in the opposite
Doppler Radar. A giant thunderstorm is moving toward a weather station at 45.0mi/h (20.1 m/s). If the station sends a radar beam of frequency 200.0 MHz toward the storm, what is the difference in
Extrasolar Planets. In the not-too-distant future, it should be possible to detect the presence of planets moving around other stars by measuring the Doppler shift in the infrared light they emit. H
How fast (as a percentage of light speed) would a star have to he moving so that the frequency of the light we receive from it is 10.0% higher than the frequency of the light it is emitting? Would it
The shock-wave cone created by the space shuttle at one instant during its reentry into the atmosphere makes an angle of 58.0° with its direction of motion. The speed of sound at this altitude is
A jet plane flies overhead at Mach 1.70 and at a constant altitude of 950 m. (a) What is the angle a of the shock-wave cone? (b) How much time after the plane passes directly overhead do you hear the
(a) Defend the following statement: "In a sinusoidal sound wave, the pressure variation given by Eq. (16.4) is greatest where the displacement given by Eq. (16.1) is zero."(b) For a sinusoidal sound
A soprano and a bass are singing a duet. While the soprano sings an A# at 932 Hz, the bass sings an A# but three octaves lower. In this concert hall, the density of air is 1.20 kg/m3 and its bulk
The sound from a trumpet radiates uniformly in all directions in 20"C air. At a distance of 5.00 m from the trumpet the sound intensity level is 52.0 dB. The frequency is 587 Hz. (a) What is the
A Thermometer. Suppose you have a tube of length L containing a gas whose temperature you want to take, but you cannot get inside the tube. One end is closed, and the other end is open but a small
A uniform 165-N bar is supported horizontally by two identical wires A and B (Fig. 16.43).Asmall185-N cube of lead is placed 3/4 of the way from A toB. The wires are each 75.0 cm long and have a mass
A person is playing a small fiute 10.75 cm long, open at one end and closed at the other, near a taut string having a fundamental frequency of 600.0 Hz. H the speed of sound is 344.0 m/s, for which
A New Musical Instrument. You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length L and diameter L/10. You have stretched a string of
An organ pipe has two successive harmonics with frequencies 1372 and 1764 Hz. (a) Is this an open or a stopped pipe? Explain. (b) What two harmonics are these? (c) What is the length of the pipe?
Longitudinal Standing Waves in a Solid Longitudinal standing waves can be produced in a solid rod by holding it at some point between the fingers of one hand and stroking it with the other band. The
(a) Determine the first three normal-mode frequencies for a pipe of length L that is closed at both ends. Explain your reasoning. (b) Use the results of part (a) to estimate the normal-mode
One type of steel has a density of 7.8 X 103 kg/m3 and a breaking stress of7.0 X 108 N/m2 • A cylindrical guitar string is to be made of 4.00 g of this steel.(a) What are the length and radius of
A long tube contains air at a pressure of 1.00 atm and a temperature of 77.0°C. The tube is open at one end and closed at the other by a movable piston. A tuning fork near the open end is vibrating
Human Hearing. The auditory canal of the human ear (see Fig. 16.4) extends about 2.5 cm from the outside ear to the eardrum. (a) Explain why the human ear is especially sensitive to sounds at
A platinum wire (density 21.4 g/cm3) is 225 µm in diameter and 0.450 m long. One end of the wire is attached to the ceiling, while a 420-g mass is attached to the other end so that the wire hangs
The frequency of the note F 4 is 349 Hz. (a) If an organ pipe is open at one end and closed at the other, what length must it have for its fundamental mode to produce this note at 20.OoC? (b) At what
A standing wave with a frequency of 1100 Hz in a column of methane (CH4.) at 20.0°C produces nodes that are 0.200 m apart. What is the value of y for methane? (The molar mass of methane is 16.0
Two identical loudspeakers are located at points A and B, 2.00 m apart. The loudspeakers are driven by the same amplifier and produce sound waves with a frequency of 784 Hz. Take the speed of sound
Wagnerian Opera. A man marries a great Wagnerian soprano but, alas, he discovers he cannot stand Wagnerian opera. In order to save his eardrums, the unhappy man decides he must silence his lark like
A hat flies toward a wall, emitting a steady sound of frequency 2.00 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the hat fly in order to hear a beat
A small sphere of radius R is arranged to pulsate so that its radius varies in simple harmonic motion between a minimum of R - ΔR and a maximum of R + ΔR with frequency f- This produces
Ultrasound in Medicine. A 2.00-MHz sound wave travels through a pregnant woman's abdomen and is reflected from the fetal heart wall of her unborn baby. The heart wall is moving toward the sound
The sound source of a ship's sonar system operates at a frequency of 22.0 kHz. The speed of sound in water (assumed to be at a uniform 20°C) is 1482 m/s. (a) What is the wavelength of the waves
A police siren of frequency fsiren is attached to a vibrating platform. The platform and siren oscillate up and down in simple harmonic motion with amplitude Ap and frequency fp. (a) Find the maximum
Horseshoe bars (genus Rhinolophus) emit sounds from their nostrils and then listen to the frequency of the sound reflected from their prey to determine the prey's speed. (The €œhorseshoe"
(a) Show that Eq. (1630) can be written as(b) Use the binomial theorem to show that if v « c, this is approximately equal tofr=fs(1-u/c) -1/2(c) A pilotless reconnaissance aircraft emits a
Supernova! The gas cloud known as the Crab Nebula can be seen with even a small telescope. It is the remnant of a supernova, a cataclysmic explosion of a star. The explosion was seen on the earth on
Weather Forecasting, A radar installation used for monitoring thunderstorms emits radio waves at a frequency of2800 MHz. A line of thunderstorms is approaching the installation at 42.0 km/h. (a) In
A woman stands at rest in front of a large, smooth wall. She holds a vibrating tuning fork of frequency 10 directly in front of her (between her and the wall). (a) The woman now runs toward the wall
On a clear day you see a jet plane flying overhead. From the apparent size of the plane, you determine that it is flying at a constant altitude h. You hear the sonic boom at time T after the plane
Figure 16.45 shows the pressure fluctuation p of a nonsinusoidal sound wave as a function of x for t = 0. The wave is traveling in the +x-direction.(a) Graph the pressure fluctuation p as a function
Two loudspeakers, A and B, radiate sound uniformly in all directions in air at 20°C. The acoustic power output from A is 8.00 X 10-4 W, and from B it is 6.00 X 10-5 W. Both loudspeakers are
Is a bouncing ball an example of simple harmonic motion? Is the daily movement of a student from home to school and back simple harmonic motion? Why or why not?
If the coordinate of a particle varies as x = -A cos wt, what is the phase constant in Equation 15.6? At what position is the particle at t = 0?
Does the displacement of an oscillating particle between t = 0 and a later time t necessarily equal the position of the particle at time t? Explain.
Determine whether or not the following quantities can be in the same direction for a simple harmonic oscillator:(a) Position and velocity, (b) Velocity and acceleration,(c) Position and acceleration.
Can the amplitude A and phase constant Ф be determined for an oscillator if only the position is specified at t = 0? Explain.
Describe qualitatively the motion of a block–spring system when the mass of the spring is not neglected.
A block is hung on a spring, and the frequency f of the oscillation of the system is measured. The block, a second identical block, and the spring are carried in the Space Shuttle to space. The two
A block–spring system undergoes simple harmonic motion with amplitude A. Does the total energy change if the mass is doubled but the amplitude is not changed? Do the kinetic and potential energies
The equations listed in Table 2.2 give position as a function of time, velocity as a function of time, and velocity as function of position for an object moving in a straight line with constant
What happens to the period of a simple pendulum if the pendulum’s length is doubled? What happens to the period if the mass of the suspended bob is doubled?
A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is determined. Describe the changes, if any, in the period when the elevator(a) Accelerates upward, (b)
Imagine that a pendulum is hanging from the ceiling of a car. As the car coasts freely down a hill, is the equilibrium position of the pendulum vertical? Does the period of oscillation differ from
A simple pendulum undergoes simple harmonic motion when θ is small. Is the motion periodic when θ is large? How does the period of motion change as θ increases?
If a grandfather clock were running slow, how could we adjust the length of the pendulum to correct the time
Will damped oscillations occur for any values of b and k? Explain.
Is it possible to have damped oscillations when a system is at resonance? Explain.
At resonance, what does the phase constant Ф equal in Equation 15.35? (Suggestion: Compare this equation with the expression for the driving force, which must be in phase with the velocity at
You stand on the end of a diving board and bounce to set it into oscillation. You find a maximum response, in terms of the amplitude of oscillation of the end of the board, when you bounce at
Some parachutes have holes in them to allow air to move smoothly through the chute. Without the holes, the air gathered under the chute as the parachutist falls is sometimes released from under the
You are looking at a small tree. You do not notice any breeze, and most of the leaves on the tree are motionless. However, one leaf is fluttering back and forth wildly. After you wait for a while,
A pendulum bob is made with a sphere filled with water. What would happen to the frequency of vibration of this pendulum if there were a hole in the sphere that allowed the water to leak out slowly?
Why is a pulse on a string considered to be transverse?
How would you create a longitudinal wave in a stretched spring? Would it be possible to create a transverse wave in a spring?
By what factor would you have to multiply the tension in a stretched string in order to double the wave speed?
When traveling on a taut string, does a pulse always invert upon reflection? Explain.
Does the vertical speed of a segment of a horizontal taut string, through which a wave is traveling, depend on the wave speed?
If you shake one end of a taut rope steadily three times each second, what would be the period of the sinusoidal wave set up in the rope?
A vibrating source generates a sinusoidal wave on a string under constant tension. If the power delivered to the string is doubled, by what factor does the amplitude change? Does the wave speed
Consider a wave traveling on a taut rope. What is the difference, if any, between the speed of the wave and the speed of a small segment of the rope?
If a long rope is hung from a ceiling and waves are sent up the rope from its lower end, they do not ascend with constant speed. Explain.
How do transverse waves differ from longitudinal waves?
When all the strings on a guitar are stretched to the same tension, will the speed of a wave along the most massive bass string be faster, slower, or the same as the speed of a wave on the lighter
If one end of a heavy rope is attached to one end of a light rope, the speed of a wave will change as the wave goes from the heavy rope to the light one. Will it increase or decrease? What happens to
If you stretch a rubber hose and pluck it, you can observe a pulse traveling up and down the hose. What happens to the speed of the pulse if you stretch the hose more tightly? What happens to the
In a longitudinal wave in a spring, the coils move back and forth in the direction of wave motion. Does the speed of the wave depend on the maximum speed of each coil?
Both longitudinal and transverse waves can propagate through a solid. A wave on the surface of a liquid can involve both longitudinal and transverse motion of elements of the medium. On the other
In an earthquake both S (transverse) and P (longitudinal) waves propagate from the focus of the earthquake. The focus is in the ground below the epicenter on the surface. The S waves travel through
In mechanics, mass less strings are often assumed. Why is this not a good assumption when discussing waves on strings?
Why are sound waves characterized as longitudinal?
If an alarm clock is placed in a good vacuum and then activated, no sound is heard. Explain.
A sonic ranger is a device that determines the distance to an object by sending out an ultrasonic sound pulse and measuring how long it takes for the wave to return after it reflects from the object.
A friend sitting in her car far down the road waves to you and beeps her horn at the same time. How far away must she be for you to calculate the speed of sound to two significant figures by
If the wavelength of sound is reduced by a factor of 2, what happens to its frequency? Its speed?
By listening to a band or orchestra, how can you determine that the speed of sound is the same for all frequencies?
In Example 17.3 we found that a point source with a power output of 80 W produces sound with an intensity of 1.00 x 10–8 W/m2, which corresponds to 40 dB, at a distance of about 16 miles. Why do

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