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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

To permit measurement of her speed, a skydiver carries a buzzer emitting a steady tone at 1 800 Hz. A friend on the ground at the landing site directly below listens to the amplified sound he
A train whistles (f = 400 Hz) sounds higher or lower in frequency depending on whether it approaches or recedes. (a) Prove that the difference in frequency between the approaching and receding
Two ships are moving along a line due east. The trailing vessel has a speed relative to a land-based observation point of 64.0 km/h, and the leading ship has a speed of 45.0 km/h relative to that
A bat, moving at 5.00 m/s, is chasing a flying insect (Fig. P17.7). If the bat emits a 40.0 kHz chirp and receives back an echo at 40.4 kHz, at what speed is the insect moving toward or away from the
A supersonic aircraft is flying parallel to the ground. When the aircraft is directly overhead, an observer sees a rocket fired from the aircraft. Ten seconds later the observer hears the sonic boom,
A police car is traveling east at 40.0 m/s along a straight road, overtaking a car ahead of it moving east at 30.0 m/s. The police car has a malfunctioning siren that is stuck at 1 000 Hz. (a)
The speed of a one-dimensional compressional wave traveling along a thin copper rod is 3.56 km/s. A copper bar is given a sharp compressional blow at one end. The sound of the blow, traveling through
A jet flies toward higher altitude at a constant speed of 1 963 m/s in a direction making an angle 0 with the horizontal (Fig. P17.64). An observer on the ground hears the jet for the first time when
A meteoroid the size of a truck enters the earth’s atmosphere at a speed of 20.0 km/s and is not significantly slowed before entering the ocean (a) What is the Mach angle of the shock wave from
An interstate highway has been built through a poor neighborhood in a city. In the afternoon, the sound level in a rented room is 80.0 dB, as 100 cars pass outside the window every minute. Late at
With particular experimental methods, it is possible to produce and observe in a long thin rod both a longitudinal wave and a transverse wave whose speed depends primarily on tension in the rod. The
A siren creates sound with a level B at a distance d from the speaker. The siren is powered by a battery that delivers a total energy E. Let e represent the efficiency of the siren. (That is, e is
The Doppler equation presented in the text is valid when the motion between the observer and the source occurs on a straight line, so that the source and observer are moving either directly toward or
Equation 17.7 states that, at distance r away from a point source with power Pav, the wave intensity is 1 = Pav / 4πr2 Study Figure 17.9 and prove that, at distance r straight in front of a
Three metal rods are located relative to each other as shown in Figure P17.71, where L1 + L2 = L3. The speed of sound in a rod is given by v = Y/P where P is the density and Y is Young€™s
The smallest wavelength possible for a sound wave in air is on the order of the separation distance between air molecules. Find the order of magnitude of the highest-frequency sound wave possible in
Two waves in one string are described by the wave functions y1 = 3.0 cos (4.0x - 1.6t) And y2 = 4.0 sin (5.0x - 2.0t) Where y and x are in centimeters and t is in seconds. Find the
Two pulses A and B are moving in opposite directions along a taut string with a speed of 2.00 cm/s. The amplitude of A is twice the amplitude of B. The pulses are shown in Figure P18.2 at t = 0.
Two pulses traveling on the same string are described by y1 = 5 / (3x ─4t)2 + 2 And y2 = ─5 / (3x + 4t ─6)2 + 2 (a) In which direction does each pulse travel? (b) At what
Two waves are traveling in the same direction along a stretched string. The waves are 90.0° out of phase. Each wave has an amplitude of 4.00 cm. Find the amplitude of the resultant wave.
Two traveling sinusoidal waves are described by the wave functions y1 = (5.00 m) sin [π (4.00x ─ 1 200t)] And y2 = (5.00 m) sin [π (4.00x ─ 1 200t ─ 0.250)] Where
Two identical sinusoidal waves with wavelengths of 3.00 m travel in the same direction at a speed of 2.00 m/s. The second wave originates from the same point as the first, but at a later time.
A series of pulses, each of amplitude 0.150 m, is sent down a string that is attached to a post at one end. The pulses are reflected at the post and travel back along the string without loss of
Two loudspeakers are placed on a wall 2.00 m apart. A listener stands 3.00 m from the wall directly in front of one of the speakers. A single oscillator is driving the speakers at a frequency of 300
Two speakers are driven by the same oscillator whose frequency is 200 Hz. They are located on a vertical pole a distance of 4.00 m from each other. A man walks straight toward the lower speaker in a
Two speakers are driven by the same oscillator whose frequency is f. They are located a distance d from each other on a vertical pole. A man walks straight toward the lower speaker in a direction
Two sinusoidal waves in a string are defined by the functions y1 = (2.00 cm) sin (20.0x ─ 32.0t) And y2 = (2.00 cm) sin (25.0x ─ 40.0t) Where y1, y2, and x are in centimeters and
Two identical speakers 10.0 m apart are driven by the same oscillator with a frequency of f = 21.5 Hz (Fig. P18.12)(a) Explain why a receiver at point A records a minimum in sound intensity from the
Two sinusoidal waves traveling in opposite directions interfere to produce a standing wave with the wave function y = (1.50 m) sin (0.400x) cos (200t) Where x is in meters and t is in seconds.
Two waves in a long string have wave functions given by y1 = (0.015 0 m) cos (x/2 ─ 40t) And y2 = (0.018 0 m) cos (x/2 + 40t) Where y1, y2, and x are in meters and t is in seconds.
Two speakers are driven in phase by a common oscillator at 800 Hz and face each other at a distance of 1.25 m. Locate the points along a line joining the two speakers where relative minima of sound
Verify by direct substitution that the wave function for a standing wave given in Equation 18.3, y = 2A sin kx cos wt Is a solution of the general linear wave equation, Equation
Two sinusoidal waves combining in a medium are described by the wave functions y1 = (3.0 cm) sin π (x + 0.60t) And y2 = (3.0 cm) sin (x ─ 0.60t) Where x is in centimeters and t is
Two waves that set up a standing wave in a long string are given by the wave functions y1 = A sin (kx ─ wt + ǿ) and y2 = A sin(kx + wt) Show (a) that the addition of the arbitrary
Find the fundamental frequency and the next three frequencies that could cause standing-wave patterns on a string that is 30.0 m long, has a mass per length of 9.00 X 10─3kg/m and is stretched
A string with a mass of 8.00 g and a length of 5.00 m has one end attached to a wall; the other end is draped over a pulley and attached to a hanging object with a mass of 4.00 kg. If the string is
In the arrangement shown in Figure P18.21, an object can be hung from a string (with linear mass density μ = 0.002 00 kg/m) that passes over a light pulley. The string is connected to a vibrator
A vibrator, pulley, and hanging object are arranged as in Figure P18.21, with a compound string, consisting of two strings of different masses and lengths fastened together end-to-end. The first
Example 18.4 tells you that the adjacent notes E, F, and Fsharp can be assigned frequencies of 330 Hz, 350 Hz, and 370 Hz. You might not guess how the pattern continues. The next notes, G, G-sharp,
The top string of a guitar has a fundamental frequency of 330 Hz when it is allowed to vibrate as a whole, along all of its 64.0-cm length from the neck to the bridge. A fret is provided for limiting
A string of length L, mass per unit length +, and tension T is vibrating at its fundamental frequency. What effect will the following have on the fundamental frequency? (a) The length of the string
A 60.000-cm guitar string under a tension of 50.000 N has a mass per unit length of 0.100 00 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies
A cello A-string vibrates in its first normal mode with a frequency of 220 Hz. The vibrating segment is 70.0 cm long and has a mass of 1.20 g. (a) Find the tension in the string. (b) Determine
A violin string has a length of 0.350 m and is tuned to concert G, with fG = 392 Hz. Where must the violinist place her finger to play concert A, with fA = 440 Hz? If this position is to remain
A sphere of mass M is supported by a string that passes over a light horizontal rod of length L (Fig. P18.29). Given that the angle is / and that f represents the fundamental frequency of standing
A copper cylinder hangs at the bottom of a steel wire of negligible mass. The top end of the wire is fixed. When the wire is struck, it emits sound with a fundamental frequency of 300 Hz. If the
A standing-wave pattern is observed in a thin wire with a length of 3.00 m. The equation of the wave is where x is in meters and t is in seconds. y = (0.002 m) sin (πx) cos (100πt)
The chains suspending a child’s swing are 2.00 m long. At what frequency should a big brother push to make the child swing with largest amplitude?
An earthquake can produce a seiche in a lake, in which the water sloshes back and forth from end to end with remarkably large amplitude and long period. Consider a seiche produced in a rectangular
The Bay of Fundy, Nova Scotia, has the highest tides in the world, as suggested in the photographs on page 452. Assume that in mid-ocean and at the mouth of the bay, the Moon’s gravity gradient and
Standing-wave vibrations are set up in a crystal goblet with four nodes and four antinodes equally spaced around the 20.0-cm circumference of its rim. If transverse waves move around the glass at 900
The overall length of a piccolo is 32.0 cm. The resonating air column vibrates as in a pipe open at both ends. (a) Find the frequency of the lowest note that a piccolo can play, assuming that the
Calculate the length of a pipe that has a fundamental frequency of 240 Hz if the pipe is (a) Closed at one end and (b) Open at both ends.
The fundamental frequency of an open organ pipe corresponds to middle C (261.6 Hz on the chromatic musical scale). The third resonance of a closed organ pipe has the same frequency. What are the
The windpipe of one typical whooping crane is 5.00 ft long. What is the fundamental resonant frequency of the bird’s trachea, modeled as a narrow pipe closed at one end? Assume a temperature of
Do not stick anything into your ear! Estimate the length of your ear canal, from its opening at the external ear to the eardrum. If you regard the canal as a narrow tube that is open at one end and
A shower stall measures 86.0 cm X 86.0 cm X 210 cm. If you were singing in this shower, which frequencies would sound the richest (because of resonance)? Assume that the stall acts as a pipe closed
As shown in Figure P18.42, water is pumped into a tall vertical cylinder at a volume flow rate R. The radius of the cylinder is r, and at the open top of the cylinder a tuning fork is vibrating with
If two adjacent natural frequencies of an organ pipe are determined to be 550 Hz and 650 Hz, calculate the fundamental frequency and length of this pipe. (Use v = 340 m/s.)
A glass tube (open at both ends) of length L is positioned near an audio speaker of frequency f = 680 Hz. For what values of L will the tube resonate with the speaker?
An air column in a glass tube is open at one end and closed at the other by a movable piston. The air in the tube is warmed above room temperature, and a 384-Hz tuning fork is held at the open end.
A tuning fork with a frequency of 512 Hz is placed near the top of the pipe shown in Figure 18.19a. The water level is lowered so that the length L slowly increases from an initial value of 20.0 cm.
When an open metal pipe is cut into two pieces, the lowest resonance frequency for the air column in one piece is 256 Hz and that for the other is 440 Hz. (a) What resonant frequency would have
With a particular fingering, a flute plays a note with frequency 880 Hz at 20.0°C. The flute is open at both ends. (a) Find the air column length. (b) Find the frequency it produces at the
An aluminum rod 1.60 m long is held at its center. It is stroked with a rosin-coated cloth to set up a longitudinal vibration. The speed of sound in a thin rod of aluminum is 5 100 m/s. (a) What is
An aluminum rod is clamped one quarter of the way along its length and set into longitudinal vibration by a variable frequency driving source, the lowest frequency that produces resonance is 4 400
In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide extra loudness. For example, the note at 110 Hz has two strings at this frequency. If one string slips
While attempting to tune the note C at 523 Hz, a piano tuner hears 2 beats/s between a reference oscillator and the string. (a) What are the possible frequencies of the string? (b) When she
A student holds a tuning fork oscillating at 256 Hz. He walks toward a wall at a constant speed of 1.33 m/s. (a) What beat frequency does he observe between the tuning fork and its echo? (b) How
When beats occur at a rate higher than about 20 per second, they are not heard individually but rather as a steady hum, called a combination tone. The player of a typical pipe organ can press a
An A-major chord consists of the notes called A, C#, and E. It can be played on a piano by simultaneously striking strings with fundamental frequencies of 440.00 Hz, 554.37 Hz, and 659.26 Hz. The
Suppose that a flutist plays a 523-Hz C note with first harmonic displacement amplitude A1 = 100 nm. From Figure 18.24b read, by proportion, the displacement amplitudes of harmonics 2 through 7. Take
On a marimba (Fig P18.57), the wooden bar that sounds a tone when struck vibrates in a transverse standing wave having three antinodes and two nodes. The lowest frequency note is 87.0 Hz, produced by
A loudspeaker at the front of a room and an identical loudspeaker at the rear of the room are being driven by the same oscillator at 456 Hz. A student walks at a uniform rate of 1.50 m/s along the
Two train whistles have identical frequencies of 180 Hz. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a
A string fixed at both ends and having a mass of 4.80 g, a length of 2.00 m, and a tension of 48.0 N vibrates in its second (n = 2) normal mode. What is the wavelength in air of the sound emitted by
A student uses an audio oscillator of adjustable frequency to measure the depth of water well. The student hears two successive resonances at 51.5 Hz and 60.0 Hz. How deep is the well?
A string has a mass per unit length of 9.00 X 10─3 kg/m and a length of 0.400 m. What must be the tension in the string if its second harmonic has the same frequency as the second resonance
Two wires are welded together end to end. The wires are made of the same material, but the diameter of one is twice that of the other. They are subjected to a tension of 4.60 N. The thin wire has a
For the arrangement shown in Figure P18.64, /θ = 30.0°, the inclined plane and the small pulley are frictionless, the string supports the object of mass M at the bottom of the plane, and
A standing wave is set up in a string of variable length and tension by a vibrator of variable frequency. Both ends of 65 the string is fixed. When the vibrator has a frequency f, in a string of
A 0.010 0-kg wire, 2.00 m long, is fixed at both ends and vibrates in its simplest mode under a tension of 200 N. When a vibrating tuning fork is placed near the wire, a beat frequency of 5.00 Hz is
Two waves are described by the wave functions y1(x, t) = 5.0 sin (2.0x ─ 10t) And y2(x, t) = 10 cos (2.0x ─ 10t) Where y1, y2, and x are in meters and t is in seconds. Show that
The wave function for a standing wave is given in Equation 18.3 as y = 2A sin kx cos wt. (a) Rewrite this wave function in terms of the wavelength ' and the wave speed v of the wave. (b) Write
A 12.0-kg object hangs in equilibrium from a string with a total length of L = 5.00 m and a linear mass density of μ = 0.001 00 kg/m. The string is wrapped around two light, frictionless pulleys
A quartz watch contains a crystal oscillator in the form of a block of quartz that vibrates by contracting and expanding. Two opposite faces of the block, 7.05 mm apart, are antinodes, moving
The speed of sound in air at 20oC is 344 m/s. (a) What is the wavelength of a sound wave with a frequency of 784 Hz, corresponding to the note 0, on a piano, and how many milliseconds does each
Audible Sound provided the amplitude is sufficiently great, the human ear can respond to longitudinal waves over a range of frequencies from about 20.0 Hz to about 20.0 kHz. (a) If you were to mark
Tsunami! On December 26, 2004, a great earthquake occurred off the coast of Sumatra and triggered immense waves (tsunami) that killed some 200,000 people. Satellites observing these waves from space
Ultrasound Imaging sound having frequencies above the range of human hearing (about 20,000 Hz) is called ultrasound. Waves above this frequency can be used to penetrate the body and to produce images
Visible Light is a wave, but not a mechanical wave. The quantities that oscillate are electric and magnetic fields. Light visible to humans has wavelengths between 400 urn (violet) and 700 urn (red),
A certain transverse wave is described byDetermine the waves(a) Amplitude;(b) Wavelength;(c) Frequency;(d) Speed of propagation;(e) Direction of propagation.
Transverse waves on a string have wave speed 8.00 m/s, amplitude 0.0700 m, and wavelength 0.320 m. The waves travel in the -x-direction, and at t = 0 the x = 0 end of the string bas its maximum
A water wave traveling in a straight line on a lake is described by the equationWhere y is the displacement perpendicular to the undisturbed surface of the lake?(a) How much time does it take for one
Which of the following wave functions satisfies the wave equation?(a)y(x, I) = A cos (kx + wt);(b)y(x, I) =A sin (kx + w,);(c) y (x, t) = A(cos kx + cos wt).(d) For the wave of part(b), write the
A wave on a string is described by y(x, t) =Acos(kx - wt). (a) Graph y, vy' and ay as functions of x for time t = 0. (b) Consider the following points on the string: (i) x = 0; (ii) x = π/4k;
A sinusoidal wave is propagating along a stretched string that lies along the x-axis. The displacement of the string as a function of time is graphed in Fig.l5.30 for particles at x = 0 and at x =
Speed of Propagation vs. Particle Speed(a) Show that Eq. (IS.3) may be written as(b) Use y(x, t) to find an expression for the transverse velocity uy of a particle in the string on which the wave
A transverse wave on a string bas amplitude 0.300 cm, wave length 12.0 cm, and speed 6.00 cm/s it is represented by y (x, t) as given in Exercise I5.12. (a) At time, t = 0, compute y at1.5-
With what tension must a rope with length 2.50 m and mass 0.120 kg be stretched for transverse waves of frequency 40.0 Hz to have a wavelength of 0.750 m?

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