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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

A piano tuner hears one beat every 2.0s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string?
What is the beat frequency if middle C (262 Hz) and C (277 Hz) are played together? What is each is played two octaves lower (each frequency reduced by a factor of 4)?
A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency
A guitar string produce 4 beats/s when sounded with a 350 Hz tuning fork what is the vibrational frequency of the string Explain your reasoning?
Two violin strings are tuned to the same frequency, 2.0%. What will be the beat frequency heard when the two strings are played together?
How many beats will be heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0oC and the other at 25.0oC?
You have three tuning forks A, B, and C. Fork B has a frequency of 441 Hz, when A and B are sounded together, a beat frequency of 3Hz is heard. When B and C are sounded together, the beat frequency
Two loudspeakers are 1.80m apart. A person stands 3.00 m from one speaker and 3.50m from the other.(a) What is the lowest frequency at which destructive interference will occur at this point?(b)
Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0s when they are played together.(a) If one is vibrating at 132 Hz, what must be the frequency of
A source emits sound of wavelengths 2.64 m and 2.76m in air. How many beats per second will be heard? (Assume T = 20oC).
The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30.0m/s(a) Toward the fire engine, and (b) Away from it?
You are standing still. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32m/s?(a) Toward you, or (b) Away from you?
(a) Compare the shift in frequency if a 2000-Hz source is moving toward you at 15m/s, versus you moving toward it at 15 m/s. Are the two frequencies exactly the same? Are they close?(b) Repeat the
Two automobiles are equipped with the same single-frequency horn. When one is at rest and the other is moving toward the first at 15m/s. The driver at rest hears a bear frequency of 5.5Hz. What is
A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25.0m/s. What is the received sound frequency?
A bat flies toward a wall at a speed of 5.0m/s. As it flies, the bat emits and ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?
In one of the original Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75Hz, and a second identical tube played the same tone while at rest in the railway station.
A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s. What is the
The Doppler effect using ultrasonic waves of frequency 2.25 X 106 Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in
A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12.0 m/s from the north, what frequency will observers hear who are located, at rests. (a) Due north,(b) Due South(c) Due
(a) How fast is an object moving on land if its speed at 20oC is Mach 0.33?(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that
An airplane travels at Mach 2.3 where the speed of sound is 310 m/s. (a) What is the angle the shock wave makes with the direction of the airplane’s motion?(b) If the plane is flying at a height of
A space probe enters the thin atmosphere if planet where the speed of sound is only about 35 m/s. (a) What is the probe’s Mach number if its initial speed is 15,000 km/h?(b) What is the angle of
A meteorite traveling 8500m/s strikes the ocean. Determine the shock wave angle it produces (a) In the air just before entering the ocean, and (b) In the water just after entering. Assume T = 20oC.
Show that the angle θ a sonic boom makes with the path of a supersonic object is given by Eq. 12-5.
You look directly overhead and see a plane exactly 1.5km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of
A fish finder uses a sonar device that sends 20,000Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200m, what
Approximately how many octaves are there in the human audible range?
A science museum has a display called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. (a) If the pipes have lengths of 3.0m, 2.5m, 2.0m, 1.5m
A single mosquito 5.0m from a person makes a sound close to the threshold of human hearing (0dB). What will be the sound level of 1000 such mosquitoes?
What is resultant sound level when an 82-dB sound and an 87-dB sound are heard simultaneously?
The sound level 12.0m from a loudspeaker, placed in the open, is 1.5 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direction?
A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output is watts at 15 kHz?
Workers around jet aircraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30m, is 140 dB, and that the average human ear
In audio and communications systems, the gain, B, in decibels is defined asWhere Pm is the power input to the system and Pout is the power output. A particular stereo amplifier puts out 100 W of
Each string on a violin is tuned to a frequency 1½ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each
The A string of a violin is 32 cm long between fixed points with fundamental frequency of 440 Hz and a mass per unit length of 6.1 x 10-4 kg/m. (a) What are the wave speed and tension in the
A tuning fork is set into vibration above a vertical open tube filled with water (Fig. 12-35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is
A 750-cm-long guitar string of mass 2.10g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode)
A highway overpass was observed to resonate as one full loop (½ λ) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of
A person hears a pure tone in the 500-1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person
Two trains emit 424-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?
The frequency of a stream train whistle as it approaches you is 538Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)>
At a race track, you can estimate the speed of cars by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a
Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?
Two loudspeakers are at opposite ends of a railroad car as it moves past a stationary observer at 10.0 m/s, as shown in Fig. 12-37. If the speakers have identical sound frequencies of 212 Hz, what is
If the velocity of blood flow in the aorta is normally about 0.32 m/s, what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood
A bat flies toward a moth at speed 6.5m/s while the moth is flying toward the bat at speed 5.0 m/s. The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat
A bat emits a series of high frequency sound pulses as it app=roaches a moth. The pulses are approximately 70.0ma apart, and each is about 3.0ms long. How far away can the moth be detected by the bat
The €œalpenhorn€ (Fig. 12-38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns
Room acoustics for stereo listening can be compromised by the presence of standing waves, which can cause acoustic “dead sports” at the locations of the pressure nodes. Consider a living room
A dramatic demonstration, called “singing rods”, involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice,
The intensity at the threshold of hearing for the human ear at a frequency of about 1000 Hz is lo = 1.0 X 10-12 W/m2, for which B, the sound level, is 0dB. The threshold of pain at the same frequency
A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude?
The wake of a speedboat is 15o in a lake where the speed of the water wave is 2.2km/h. What is the speed of the boat?
How long will it take sound waves to travel the distance l between the points A and B if the air temperature between them varies linearly from T1 to T2? The velocity of sound propagation in air is
A plane harmonic wave with frequency co propagates at a velocity v in a direction forming angles a, β, γ with the x, y, z axes. Find the phase difference between the oscillations at the
A plane wave of frequency co propagates so that a certain phase of oscillation moves along the x, y, z axes with velocities v1, v2, v3 respectively. Find the wave vector k, assuming the unit vectors
A plane elastic wave ε a cos (wt – kx) propagates in a medium K. Find the equation of this wave in a reference frame K' moving in the positive direction of the x axis with a constant velocity
Demonstrate that any differentiable function f (t + ax), where a is a constant, provides a solution of wave equation. What is the physical meaning of the constant a?
The equation of a travelling plane sound wave has the form ε = 60 cos (1800t – 5.3x), where ε is expressed in micrometers, t in seconds, and x in meters. Find: (a) The ratio of the
A plane wave ε = a cos (cot – kx) propagates in a homogeneous elastic medium. For the moment t = 0 draw. (a) The plots of ε, ∂ε /∂t, and ∂ε /∂x vs x;
A plane elastic wave ε = ae-yx co, and k are constants, propagates in a homogeneous medium. Find the phase difference between the oscillations at the points where the particles' displacement
Find the radius vector defining the position of a point source of spherical waves if that source is known to be located on the straight line between the points with radius vectors r1 and r2 at which
A point isotropic source generates sound oscillations with frequency v = 1.45 kHz. At a distance ro = 5.0 m from the source the displacement amplitude of particles of the medium is equal to a o =
Two plane waves propagate in a homogeneous elastic medium, one along the x axis and the other along the y axis: ε1 = a cos (wt – kx), ε2 = a cos (wt – ky) Find the wave motion pattern
A plane un-damped harmonic wave propagates in a medium. Find the mean space density of the total oscillation energy if at any point of the medium the space density of energy becomes equal to w o
A point isotropic sound source is located on the perpendicular to the plane of a ring drawn through the centre O of the ring. The distance between the point O and the source is l = |.00 m, the radius
A point isotropic source with sonic power P = 0.10 W is located at the centre of a round hollow cylinder with radius R = 1.0 m and height h = 2.0 m. Assuming the sound to be completely absorbed by
The equation of a plane standing wave in a homogeneous elastic medium has the form ε = a cos kx cos wt. Plot: (a) ε and ∂ε/∂x as functions of x at the moments t = 0 and t
A longitudinal standing wave ε = a cos kx ∙ cos (or is maintained in a homogeneous medium of density p. Find the expressions for the space density of (a) Potential energy wp (x, t);
A string 120 cm in length sustains a standing wave, with the points of the string at which the displacement amplitude is equal to 3.5 mm being separated by 15.0 cm. Find the maximum displacement
Find the ratio of the fundamental tone frequencies of two identical strings after one of them was stretched by η = 2.0% and the other, by η = 4.0%. The tension is assumed to be proportional
Determine in what way and how many times will the fundamental tone frequency of a stretched wire change if its length is shortened by 35% and the tension increased by 70%.
To determine the sound propagation velocity in air by acoustic resonance technique one can use a pipe with a piston and a sonic membrane closing one of its ends. Find the velocity of sound if the
Find the number of possible natural oscillations of air column in a pipe whose frequencies lie below vo = 1250 Hz. The length of the pipe is l = 85 cm. The velocity of sound is v = 340 m/s. Consider
A copper rod of length l = 50 cm is clamped at its midpoint. Find the number of natural longitudinal oscillations of the rod in the frequency range from 20 to 50 kHz. What are those frequencies equal
A string of mass m is fixed at both ends. The fundamental tone oscillations are excited with circular frequency w and maximum displacement amplitude a max. Find: (a) The maximum kinetic energy of the
A standing wave ε = a sin kx ∙ cos wt is maintained in a homogeneous rod with cross-sectional area S and density p. Find the total mechanical energy confined between the sections
A source of sonic oscillations with frequency vo = 1000 Hz moves at right angles to the wall with a velocity u = 0.17 m/s. Two stationary receivers R1 and R2 are located on a straight line,
A stationary observer receives sonic oscillations from two tuning forks one of which approaches, and the other recedes with the same velocity. As this takes place, the observer hears the beatings
A receiver and a source of sonic oscillations of frequency vo = 2000 Hz are located on the x axis. The source swings harmonically along that axis with a circular frequency w and an amplitude a = 50
A source of sonic oscillations with frequency Vo = 1700 Hz and a receiver are located at the same point. At the moment t = 0 the source starts receding from the receiver with constant acceleration w
A source of sound with natural frequency vo = 1.8 kHz moves uniformly along a straight line separated from a stationary observer by a distance l = 250 m. The velocity of the source is equal to η
A stationary source sends forth monochromatic sound. A wall approaches it with velocity u = 33 cm/s. The propagation velocity of sound in the medium is v = 330 m/s. In what way and how much, in per
A source of sonic oscillations with frequency Vo = 1700 Hz and a receiver are located on the same normal to a wall. Both the source and the receiver are stationary, and the wall recedes from the
Find the damping coefficient γ of a sound wave if at distances r1 = 10 m and r2 = 20 m from a point isotropic source of sound the sound wave intensity values differ by a factor η = 4.5.
A plane sound wave propagates along the x axis. The damping coefficient of the wave is γ = 0.0230 m-1. At the point x = 0 the loudness level is L = 60 dB. Find: (a) The loudness level at a
At a distance r2 = 20.0 m from a point isotropic source of sound the loudness level Lo = 30.0 dB. Neglecting the damping of the sound wave, find: (a) The loudness level at a distance r = 10.0 m from
An observer A located at a distance rA = 5.0 m from a ringing tuning fork notes the sound to fade away τ = 19s later than an observer B who is located at a distance rB = 50 m from the tuning
A plane longitudinal harmonic wave propagates in a medium with density p. The velocity of the wave propagation is v. Assuming that the density variations of the medium, induced by the propagating
A ball of radius R = 50 cm is located in the way of propagation of a plane sound wave. The sonic wavelength is λ = 20 cm, the frequency is v = 1700 Hz, the pressure oscillation amplitude in air
A point A is located at a distance r = 1.5 m from a point isotropic source of sound of frequency = 600 Hz. The sonic power of the source is P = 0.80 W. Neglecting the damping of the waves and
At a distance r = 100 m from a point isotropic source of sound of frequency 200 Hz the loudness level is equal to L = 50 dB. The audibility threshold at this frequency corresponds to the sound
Due to a certain cause the free electrons in a plane copper plate shifted over a small distance x at right angles to its surface. As a result, a surface charge and a corresponding restoring force
An oscillating circuit consisting of a capacitor with capacitance C and a coil of inductance L maintains free un-damped oscillations with voltage amplitude across the capacitor equal to For an
An oscillating circuit consists of a capacitor with capacitance C, a coil of inductance L with negligible resistance, and a switch. With the switch disconnected, the capacitor was charged to a
In an oscillating circuit consisting of a parallel-plate capacitor and an inductance coil with negligible active resistance the oscillations with energy W are sustained. The capacitor plates were
In an oscillating circuit shown in Fig. 4.27 the coil inductance is equal to L = 2.5 mH and the capacitor have capacitances C1 = 2.0μF and C2 = 3.0μF. The capacitors were charged to a voltage V
An electric circuit shown in Fig. 4.28 has a negligibly small active resistance. The left-hand capacitor was charged to a voltage Vo and then at the moment t = 0 the switch Sw was closed. Find the

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