Quiz 13: Vibrations and Waves
Physics & Astronomy
Q 1Q 1
If the amplitude of a particle in SHM is doubled, how are (a) the total energy and (b) the maximum speed affected
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(a)
The expression for the total energy of the particle executing Simple harmonic motion is,
Here, m is the mass of the particle,
is the angular frequency of oscillation, and
is the amplitude of the particle.
From the above expression, keeping the other parameters constant, it is clear that the total energy of the particle in the simple harmonic motion is directly proportional to the square of the amplitude of the particle.
Therefore, if the amplitude of a particle in the simple harmonic motion is doubled, then the total energy of the particle will be four times its initial energy.
(b)
The expression for the maximum speed of the particle in simple harmonic motion is,
Since, the maximum speed of the particle is directly proportional to the amplitude of the particle. Therefore, if the amplitude of the particle is doubled then the speed of the particle will also be doubled.
Q 2Q 2
A particle oscillates in SHM with an amplitude A. What is the total distance (in terms of A ) the particle travels in three periods
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The amplitude of a particle is the maximum displacement produced by that particle in a simple harmonic motion. For one period, the particle travels a distance which is equal to 4 times its amplitude.
Calculate the distance of the particle in 3 periods as follows:
Thus, the particle travels in 3 periods is
.
Q 3Q 3
For a particle in SHM, the force on it ( F ) and its displacement from its equilibrium position ( x ) are (a) in the same direction, (b) opposite in direction, (c) perpendicular to each other, (d) none of the preceding.
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Multiple Choice
In simple harmonic motion, the particle moves again and again over the same path about a fixed point (equilibrium position). SHM is defined as the motion of an oscillatory particle which is acted upon by a restoring force
, which is directly proportional to the displacement
and opposite in direction.
Hence, the correct answer is option
.
Q 4Q 4
How does the speed of a mass in SHM change as the mass leaves its equilibrium position Explain.
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Q 5Q 5
If it takes a particle in SHM 0.50 s to travel from the equilibrium position to the maximum displacement (amplitude), what is the period of oscillation
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Q 6Q 6
The maximum kinetic energy of a mass-spring system in SHM is equal to (a) A , (b) A 2 , (c) kA , (d) kA 2 /2.
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Q 7Q 7
A mass-spring system in SHM has an amplitude A and period T. How long does the mass take to travel a distance A How about 2 A
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Q 8Q 8
A 0.75-kg object oscillating on a spring completes a cycle every 0.50 s. What is the frequency of this oscillation
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Q 9Q 9
If the frequency of a system in SHM is doubled, the period of the system is (a) doubled, (b) halved, (c) four times as large, (d) one-quarter as large.
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Q 10Q 10
A tennis player uses a racket to bounce a ball up and down with a constant period. Is this a simple harmonic motion Explain.
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Q 11Q 11
A particle in simple harmonic motion has a frequency of 40 Hz. What is the period of this oscillation
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Q 12Q 12
When a particle in a horizontal SHM is at the equilibrium position, the kinetic energy of the system is (a) zero, (b) at a maximum, (c) half the maximum value, (d) none of the preceding.
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Q 13Q 13
If a mass-spring system were taken to the Moon, would the period of the system change How about the period of a pendulum taken to the Moon Explain.
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Q 14Q 14
The frequency of a simple harmonic oscillator is doubled from 0.25 Hz to 0.50 Hz. What is the change in its period
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Q 15Q 15
The equation of motion for a particle in SHM (a) is a sine or cosine function, (b) is a tangent or cotangent function, (c) could be any mathematical function, (d) gives the velocity of the particle as a function of time.
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Multiple Choice
Q 16Q 16
If you want to increase the frequency of vibration of a mass-spring system, would you increase or decrease the mass Explain.
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Q 17Q 17
An object of mass 0.50 kg is attached to a spring with spring constant 10 N/m. If the object is pulled down 0.050 m from the equilibrium position and released, what is its maximum speed
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Q 18Q 18
For the SHM equation y = A sin[(200 rad/s) t ], the frequency of oscillation, f , is (a) 50 Hz, (b) 100 Hz, (c) 200 Hz, (d) 200 Hz.
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Q 20Q 20
An object of mass 1.0 kg is attached to a spring with spring constant 15 N/m. If the object has a maximum speed of 0.50 m/s, what is the amplitude of oscillation
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Q 21Q 21
A mass-spring system in SHM has an amplitude A and period T. How long does the mass take to travel a distance A How about 2 A
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Q 22Q 22
Would the period of a pendulum in an upward-accelerating elevator be increased or decreased compared with its period in a nonaccelerating elevator Explain.
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Q 23Q 23
Atoms in a solid are in continuous vibrational motion due to thermal energy. At room temperature, the amplitude of these atomic vibrations is typically about 10 - 9 cm, and their frequency is on the order of 10 12 Hz. (a) What is the approximate period of oscillation of a typical atom (b) What is the maximum speed of such an atom
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Q 24Q 24
Wave motion in a material medium involves (a) the propagation of a disturbance, (b) interparticle interactions, (c) the transfer of energy, (d) all of the preceding.
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Q 25Q 25
One simple harmonic motion is described by a sine function, y = A sin ( t ), and another is described by a cosine function, y = A cos ( t ). Discuss the differences in their initial position, velocity, and acceleration.
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Q 26Q 26
A particle of mass 0.10 kg is attached to a spring of spring constant 10 N/m. If the maximum acceleration of the particle is 5.0 m/s 2 , what is the maximum speed of the particle
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Q 27Q 27
For a longitudinal wave, the direction between the wave velocity and particle oscillation is (a) perpendicular, (b) parallel, (c) 45°, or (d) none of the preceding.
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Q 28Q 28
When a wave pulse travels along a rope, what travels with the wave motion and what does not travel with the wave
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Q 29Q 29
(a) At what position is the magnitude of the force on a mass in a mass-spring system minimum: (1) x = 0, (2) x = A , or (3) x = + A Why (b) If m = 0.500 kg, k = 150 N/m, and A = 0.150 m, what are the magnitude of the force on the mass and the acceleration of the mass at x = 0,0.050 m, and 0.150 m
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Q 30Q 30
A water wave is (a) transverse, (b) longitudinal, (c) a combination of transverse and longitudinal, (d) none of the preceding.
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Q 31Q 31
Figure shows pictures of two mechanical waves. Identify each as being transverse or longitudinal.
FIGURE Transverse or longitudinal See Conceptual Exercise.
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Q 32Q 32
(a) At what position is the speed of a mass in a mass-spring system maximum: (1) x = 0, (2) x = A , or (3) x = + A Why (b) If m = 0.250 kg, k = 100 N/m, and A = 0.10 m for such a system, what is the mass's maximum speed
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Q 33Q 33
When two waves meet each other and interfere, the resultant waveform is determined by (a) reflection, (b) refraction, (c) diffraction, (d) superposition.
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Q 34Q 34
What type(s) of wave(s), transverse or longitudinal, will propagate through (a) solids, (b) liquids, and (c) gases
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Q 35Q 35
A mass-spring system is in SHM in the horizontal direction. If the mass is 0.25 kg, the spring constant is 12 N/m, and the amplitude is 15 cm, (a) what is the maximum speed of the mass, and (b) where does this occur (c) What is the speed at a half-amplitude position
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Q 36Q 36
When two identical waves of the same wavelength ( ) and amplitude ( A ) interfere in phase, the amplitude of the resulting wave is (a) A , (b) 2 A , (c) 3 A , (d) 4 A.
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Multiple Choice
Q 37Q 37
Standing on a hill and looking at a tall wheat field, you see a beautiful wave traveling across the field whenever a breeze blows. What type of wave is this Explain.
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Q 38Q 38
A horizontal spring on a frictionless level air track has a 0.150-kg object attached to it and it is stretched 6.50 cm. Then the object is given an outward initial velocity of 2.20 m/s. if the spring constant is 35.2 N/m, determine how much farther the spring stretches.
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Q 39Q 39
You can often hear people talking from around a corner of a building. This is due primarily to (a) reflection, (b) refraction, (c) interference, (d) diffraction.
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Q 40Q 40
What is cancelled out when destructive interference occurs What happens to the wave energy in such a situation Explain.
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Q 41Q 41
A 0.25-kg object is suspended on a light spring of spring constant 49 N/m. The spring is then compressed to a position 15 cm above the stretched equilibrium position. How much more energy does the system have at the compressed position than at the stretched equilibrium position
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Q 42Q 42
For two traveling waves to form standing waves, the waves must have the same (a) wavelength, (b) amplitude, (c) speed, (d) all of the preceding.
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Q 43Q 43
Dolphins and bats determine the location of their prey by emitting ultrasonic sound waves. Which wave phenomenon is involved
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Q 44Q 44
A 0.25-kg object is suspended on a light spring of spring constant 49 N/m and the system is allowed to come to rest at its equilibrium position. The object is then pulled down 0.10 m from the equilibrium position and released. What is the speed of the object when it goes through the equilibrium position
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Q 45Q 45
The points of zero amplitude on a rope that is supporting a standing wave waveform are called (a) nodes, (b) antinodes, (c) fundamentals, (d) resonance points.
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Q 46Q 46
If sound waves were dispersive (that is, if the speed of sound depended on its frequency), what would be the consequences of someone listening to an orchestra in a concert hall
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Q 47Q 47
A 0.350-kg block moving vertically upward collides with a light vertical spring and compresses it 4.50 cm before coming to rest. If the spring constant is 50.0 N/m, what was the initial speed of the block (Ignore energy losses to sound and other factors during the collision.)
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Q 48Q 48
For a standing wave on a rope, the distance between two adjacent antinodes is (a) 1/4 wavelength, (b) 1/2 wavelength, (c) one wavelength, (d) two wavelengths.
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Q 49Q 49
Can harmonic sound of any frequency be generated and heard from a violin string with a fixed tension Explain.
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Q 50Q 50
A 75-kg circus performer jumps from a 5.0-m height onto a trampoline and stretches it downward 0.30 m. Assuming that the trampoline obeys Hooke's law, (a) how far will it stretch if the performer jumps from a height of 8.0 m (b) How far will the trampoline stretch if the performer stands still on it while taking a bow
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Q 51Q 51
When a stretched violin string oscillates in its second harmonic mode, the standing wave in the string will exhibit (a) 1/4 wavelength, (b) 1/2 wavelength, (c) one wavelength, (d) two wavelengths.
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Q 52Q 52
If they have the same tension and length, will a thicker or a thinner guitar string sound higher in frequency Why
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Q 53Q 53
A vertical spring has a 0.200-kg mass attached to it. The mass is released from rest and falls 22.3 cm before stopping. (a) Determine the spring constant. (b) Determine the speed of the mass when it has fallen only 10.0 cm.
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Q 54Q 54
A child's swing (a pendulum) has only one natural frequency, f 1 , yet it can be driven or pushed smoothly at frequencies of f 1 /2, f 1 /3, and 2 f 1. How is this possible
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Q 55Q 55
A 0.250-kg ball is dropped from a height of 10.0 cm onto a spring, as illustrated in Fig. If the spring has a spring constant of 60.0 N/m, (a) what distance will the spring be compressed (Neglect energy loss during collision.) (b) On recoiling upward, how high will the ball go
FIGURE How far down See Exercise.
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Q 56Q 56
By rubbing the circular lip of a wide, thin wine glass with a moist finger, you can make the glass "sing." (Try it.) (a) What causes liais (b) What would happen to the frequency of the sound if you added water to the glass
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Q 57Q 57
A 0.50-kg mass oscillates in simple harmonic motion on a spring with a spring constant of 200 N/m. What are (a) the period and (b) the frequency of the oscillation
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Q 58Q 58
The equation of motion of a particle in vertical SHM is given by y = (10 cm) sin[(0.50 rad/s) t ]. What are the particle's (a) displacement, (b) velocity, and (c) acceleration at t = 1.0 s
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Q 59Q 59
How much mass should be at the end of a spring ( k = 100 N/m) in order to have a period of 2.0 s
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Q 60Q 60
If the frequency of a mass-spring system is 1.50 Hz and the mass on the spring is 5.00 kg, what is the spring constant
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Q 61Q 61
A breeze sets a suspended lamp into oscillation. If the period is 1.0 s, what is the distance from the ceiling to the lamp at the lowest point Assume that the lamp is a point mass and acts as a simple pendulum.
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Q 62Q 62
Write the general equation of motion for a mass that is on a horizontal frictionless surface and is connected to a spring at equilibrium (a) if the mass is initially pulled in the + x axis from the spring (stretched) and released, and (b) if the mass is pushed in the x axis toward the spring (compressed) and released.
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Q 63Q 63
The equation of motion for an oscillator in vertical SHM is given by y = (0.10 m) sin[(100 rad/s) t ]. What are the (a) amplitude, (b) frequency, and (c) period of this motion
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Q 64Q 64
The displacement of an object is given by y = (5.0 cm) cos[ (20 rad/s) t ]. What are the object's (a) amplitude, (b) frequency, and (c) period of oscillation
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Q 65Q 65
If the displacement of an oscillator in SHM is described by the equation y = (0.25 m) cos[(314 rad/s) t ], where y is in meters and t is in seconds, what is the position of the oscillator at (a) t = 0, (b) t = 5.0 s, and (c) t = 15 s
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Q 66Q 66
Tire equation of motion of a SHM oscillator is x = (0.50 m) sin(2 f ) t , where x is in meters and t is in seconds. If the position of the oscillator is at x = 0.25 m at t = 0.25 s, what is the frequency of the oscillator
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Q 67Q 67
The oscillations of two oscillating mass-spring systems are graphed in Fig. The mass in System A is four times that in System B. (a) Compared with System B, System A has (1) more, (2) the same, or (3) less energy. Why (b) Calculate the ratio of energy between System B and System A.
FIGURE Wave energy and equation of motion See Exercise.
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Q 69Q 69
Show that for a pendulum to oscillate at the same frequency as a mass on a spring, the pendulum's length must be given by L = mg / k.
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Q 70Q 70
The velocity of a vertically oscillating mass-spring system is given by v = (0.650 m/s) sin[(4 rad/s) t ]. Determine (a) the amplitude and (b) the maximum acceleration of this oscillator.
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Q 71Q 71
(a) If the mass in a mass-spring system is halved, the new period is (1) 2, (2)
, (3)
, (4) 1/2 times the old period. Why (b) If the initial period is 3.0 s and the mass is reduced to 1/3 of its initial value, what is the new period
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Q 72Q 72
(a) If the spring constant in a mass-spring system is halved, the new period is (1) 2, (2)
, (3)
, (4) 1/2 limes the old period. Why (b) If the initial period is 2.0 s and the spring constant is reduced to 1/3 of its initial value, what is the new period
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Q 73Q 73
Students use a simple pendulum with a length of 36.90 cm to measure the acceleration of gravity at the location of their school. If it takes 12.20 s for the pendulum to complete ten oscillations, what is the experimental value of g at the school
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Q 74Q 74
The equation of motion of a particle in vertical SHM is given by y = (10 cm) sin[(0.50 rad/s) t ]. What are the particle's (a) displacement, (b) velocity, and (c) acceleration at t = 1.0 s
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Q 75Q 75
What is the maximum elastic potential energy of a simple horizontal mass-spring oscillator whose equation of motion is given by x = (0.350 m) sin[( 7 rad/s) t ] The mass on the end of the spring is 0.900 kg.
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Q 76Q 76
Two masses oscillate on light springs. The second mass is half of the first and its spring constant is twice that of the first. Which system will have the greater frequency, and what is the ratio of the frequency of the second mass to that of the first mass
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Q 77Q 77
During an earthquake, the floor of an apartment building is measured to oscillate in approximately simple harmonic motion with a period of 1.95 seconds and an amplitude of 8.65 cm. Determine the maximum speed and acceleration of the floor during this motion.
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Q 78Q 78
(a) If a pendulum clock were taken to the Moon, where the acceleration due to gravity is only one-sixth (assume the figure to be exact) that on the Earth, will the period of vibration (1) increase, (2) remain the same, or (3) decrease Why (b) If the period on the Earth is 2.0 s, what is the period on the Moon
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Q 79Q 79
The motion of a particle is described by the curve for System A in Fig. (a) Write the equation of motion in terms of a sine or cosine function. (b) If the spring constant is 20 N/m, what is the mass of the object
FIGURE Wave energy and equation of motion See Exercise.
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Q 80Q 80
The motion of a 0.25-kg mass oscillating on a light spring is described by the curve for System B in Fig. (a) Write the equation for the displacement of the mass as a function of time. (b) What is the spring constant of the spring
FIGURE Wave energy and equation of motion See Exercise.
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Q 81Q 81
The forces acting on a simple pendulum are shown in Fig. (a) Show that, for the small angle approximation (sin ), the force producing the motion has the same form as Hooke's law. (b) Show by analogy with a mass on a spring that the period of a simple pendulum is given by T = 2
. [ Hint : Think of the effective spring constant.]
FIGURE SHM of a pendulum See Exercise.
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Q 82Q 82
The acceleration as a function of time of a mass-spring system is given by a = (0.60 m/s 2 ) sin[ (2 rad/s) t ]. If the spring constant is 10 N/m, what are (a) the amplitude, (b) the initial velocity and (c) the mass of the object
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Q 83Q 83
A clock uses a pendulum that is 75 cm long. The clock is accidentally broken, and when it is repaired, the length of the pendulum is shortened by 2.0 mm. Consider the pendulum to be a simple pendulum. (a) Will the repaired clock gain or lose time (b) By how much will the time indicated by the repaired clock differ from the correct time (taken to be the time determined by the original pendulum in 24 h) (c) If the pendulum rod were metal, would the surrounding temperature make a difference in the timekeeping of the clock Explain.
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Q 84Q 84
The velocity of a vertically oscillating 5.00-kg mass on a spring is given by v = ( 0.600 m/s) sin[(6 rad/s) t ]. (a) Determine the equation of motion ( y ). (b) Where does the motion start and in what direction does the object move initially and with what speed (c) Determine the period of the motion. (d) Determine the maximum force on the mass.
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Q 85Q 85
A sound wave has a speed of 340 m/s in air. If this wave produces a tone with a frequency of 1000 Hz, what is its wavelength
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Q 86Q 86
A wave on a rope that measures 10 m long takes 2.0 s to travel the whole rope. If the wavelength of the wave is 2.5 m, what is the frequency of oscillation of any piece of the rope
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Q 87Q 87
A student reading his physics book on a lake dock notices that the distance between two incoming wave crests is about 0.75 m, and he then measures the time of arrival between the crests to be 1.6 s. What is the approximate speed of the waves
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Q 88Q 88
Dolphins and bats determine the location of their prey using echolocation (see Conceptual Question). If it takes 15 ms for a bat to receive the ultrasonic sound wave reflected off a mosquito, how far is the mosquito from the bat Take the speed of sound as 345 m/s.
Conceptional Question
Dolphins and bats determine the location of their prey by emitting ultrasonic sound waves. Which wave phenomenon is involved
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Q 89Q 89
Light waves travel in a vacuum at a speed of 3.00 × 10 8 m/s. The frequency of blue light is about 6 × 10 14 Hz. What is the approximate wavelength of the light
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Q 90Q 90
A sonar generator on a submarine produces periodic ultrasonic waves at a frequency of 2.50 MHz. The wavelength of the waves in seawater is 4.80 × 10 - 4 m. When the generator is directed downward, an echo reflected from the ocean floor is received 10.0 s later. How deep is the ocean at that point
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Q 91Q 91
The range of sound frequencies audible to the human ear extends from about 20 Hz to 20 kHz. If the speed of sound in air is 345 m/s, what are the wavelength limits of this audible range
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Q 92Q 92
The AM frequencies on a radio dial range from 550 kHz to 1600 kHz, and the FM frequencies range from 88.0 MHz to 108 MHz. All of these radio waves travel at aspeed of 3.00 × 10 8 m/s (speed of light). (a) Compared with the FM frequencies, the AM frequencies have (1) longer, (2) the same, or (3) shorter wavelengths. Why (b) What are the wavelength ranges of the AM band and the FM band
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Q 93Q 93
Fig. a shows a snapshot of a wave traveling on a rope, and Fig. b describes the position as a function of time of a point on the rope. (a) What is the amplitude of the traveling wave (b) What is the wavelength of the wave (c) What is the period of the wave (d) What is the wave speed
FIGURE How high and how fast See Exercise.
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Q 94Q 94
Assume that P and S (primary and secondary) waves from an earthquake with a focus near the Earth's surface travel through the Earth at nearly constant but different average speeds. A monitoring station that is 1000 km from the epicenter detected the S wave to arrive at 42 s after the arrival of the P wave. If the P wave has an average speed of 8.0 km/s, what is the average speed of the S wave
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Q 95Q 95
The speed of longitudinal waves traveling in a long, solid rod is given by
, where Y is Young's modulus and is the density of the solid. If a disturbance has a frequency of 40 Hz, what is the wavelength of the waves it produces in (a) an aluminum rod and (b) a copper rod [ Hint : See Tables 9.1 and 9.2.]
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Q 96Q 96
Fred strikes a steel train rail with a hammer at a frequency of 2.50 Hz, and Wilma puts her ear to the rail 1.0 km away. (a) Flow long after the first strike does Wilma hear the sound (b) What is the time interval between the successive sound pulses she hears [ Hint : See Tables 9.1 and 9.2 and Exercise.]
Exercise
The speed of longitudinal waves traveling in a long, solid rod is given by
, where Y is Young's modulus and is the density of the solid. If a disturbance has a frequency of 40 Hz, what is the wavelength of the waves it produces in (a) an aluminum rod and (b) a copper rod [ Hint : See Tables 9.1 and 9.2.]
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Q 97Q 97
Refer to the wave shown in Fig. (Exercise). (a) Locate the points on the rope that have a maximum speed. Determine (b) the maximum speed, and (c) the distance between successive high and low spots on the string.
FIGURE How high and how fast See Exercise.
Exercise
Fig. a shows a snapshot of a wave traveling on a rope, and Fig. b describes the position as a function of time of a point on the rope. (a) What is the amplitude of the traveling wave (b) What is the wavelength of the wave (c) What is the period of the wave (d) What is the wave speed
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Q 98Q 98
If the frequency of the third harmonic of a vibrating string is 600 Hz, what is the frequency of the first harmonic
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Q 99Q 99
The fundamental frequency of a stretched string is 150 Hz. What are the frequencies of (a) the second harmonic and (b) the third harmonic
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Q 100Q 100
If the frequency of the fifth harmonic of a vibrating string is 425 Hz, what is the frequency of the second harmonic
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Q 101Q 101
A standing wave is formed in a stretched string that is 3.0 m long. What are the wavelengths of (a) the first harmonic and (b) the second harmonic
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Q 102Q 102
If the wavelength of the third harmonic on a string is 5.0 m, what is the length of the string
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Q 103Q 103
A piece of steel string is under tension. (a) If the tension doubles, the transverse wave speed (1) doubles, (2) halves, (3) increases by
, (4) decreases by
. Why (b) If the linear mass density of a 10.0-m length of string is 0.125 kg/m and it is under a tension of 9.00 N, what is the transverse wave speed in the string (c) What are its waves' natural frequencies
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Q 104Q 104
On a violin, a correctly tuned A string has a frequency of 440 Hz. If an A string produces sound at 450 Hz under a tension of 500 N, what should the tension be to produce the correct frequency
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Q 105Q 105
Will a standing wave be formed in a 4.0-m length of stretched string that transmits waves at a speed of 12 m/s if it is driven at a frequency of (a) 15 Hz or (b) 20 Hz
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Q 106Q 106
Two waves of equal amplitude and frequency of 250 Hz travel in opposite directions at a speed of 150 m/s in a string. If the string is 0.90 m long, for which harmonic mode is the standing wave set up in the string
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Q 107Q 107
A university physics professor buys 100 m of string and determines its total mass to be 0.150 kg. This string is used to set up a standing wave laboratory demonstration between two posts 3.0 m apart. If the desired second harmonic frequency is 35 Hz, what should be the required string tension
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Q 108Q 108
String A has twice the tension but half the linear mass density as string B, and both strings have the same length. (a) The frequency of the first harmonic on string A is (1) four times, (2) twice, (3) half, (4) 1/4 times that of string B. Explain. (b) If the lengths of the strings are 2.5 m and the wave speed on string A is 500 m/s, what are the frequencies of the first harmonic on both strings
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Q 109Q 109
You are setting up two standing string waves. You have a length of uniform piano wire that is 3.0 m long and has a mass of 0.150 kg. You cut this into two lengths, one of 1.0 m and the other of 2.0 m, and place each length under tension. What should be the ratio of tensions (expressed as short to long) so that their fundamental frequencies are the same
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Q 110Q 110
A violin string is tuned to a certain frequency (first harmonic or the fundamental frequency). (a) If a violinist wants a higher frequency, should the string be (1) lengthened, (2) kept the same length, or (3) shortened Why (b) If the string is tuned to 520 Hz and the violinist puts a finger down on the string one-eighth of the string length from the neck end, what is the frequency of the string when the instrument is played this way
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Q 111Q 111
A tight uniform string with a length of 1.80 m is tied down at both ends and placed under a tension of 100 N. When it vibrates in its third harmonic (draw a sketch), the sound given off has a frequency of 75.0 Hz. What is the mass of the string
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Q 112Q 112
In a common laboratory experiment on standing waves, the waves are produced in a stretched string by an electrical vibrator that oscillates at 60 Hz (Fig.). The string runs over a pulley, and a hanger is suspended from the end. The tension in the string is varied by adding weights to the hanger. If the active length of the string (the part that vibrates) is 1.5 m and this length of the string has a mass of 0.10 g, what masses must be suspended to produce the first four harmonics in that length
FIGURE Standing waves on strings Twin vibrating strings with standing waves. This demonstration model allows you to vary the string's tension, length, and type (linear mass density). Also, the vibration frequency can be adjusted. See Exercise.
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Q 113Q 113
A student uses a 2.00-m-long steel string with a diameter of 0.90 mm for a standing wave experiment. Tire tension on the string is tweaked so that the second harmonic of this string vibrates at 25.0 Hz. (a) Calculate the tension the string is under. (b) Calculate the first harmonic frequency for this string. (c) If you wanted to increase the first harmonic frequency by 50%, what would be the tension in the string [ Hint : See Table 9.2]
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Q 114Q 114
To study the effects of acceleration on the period of oscillation, a student puts a grandfather clock with a 0.9929-m-long pendulum inside an elevator. Find the period of the grandfather clock (a) when the elevator is stationary, (b) when the elevator is accelerating upward at 1.50 m/s 2 , (c) when the elevator is accelerating downward at 1.50 m/s 2 , (d) when the cable on the elevator breaks and the elevator simply falls, and (e) when the elevator is moving upward at a constant speed of 5.00 m/s.
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Q 115Q 115
A 0.500-kg mass is attached to a vertical spring and the system is allowed to come to equilibrium. The mass is then given an initial downward speed of 1.50 m/s. The mass travels downward 25.3 cm before stopping and returning. (a) Determine the spring constant. (b) What is its speed after it falls 15.0 cm (c) What is the acceleration of the mass at the very bottom of the motion
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Q 116Q 116
During an earthquake, a house plant of mass 15.0 kg in a tall building oscillates with a horizontal amplitude of 10.0 cm at 0.50 Hz. What are the magnitudes of (a) the maximum velocity, (b) the maximum acceleration, and (c) the maximum force on the plant (Assume SHM.)
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Q 117Q 117
A 2.0-kg mass resting on a horizontal frictionless surface is connected to a fixed spring. The mass is displaced 16 cm from its equilibrium position and released. At t = 0.50 s, the mass is 8.0 cm from its equilibrium position (and has not passed through it yet). (a) What is the period of oscillation of the mass (b) What are the speed of the mass and the force on the mass at t = 0.50 s
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Q 118Q 118
A simple pendulum is set into small-angle motion, making a maximum angle with the vertical of 5°. Its period is 2.21 s. (a) Determine its length. (b) Determine its maximum speed. (c) What is the acceleration of the pendulum bob when it is at the lowest position
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Q 119Q 119
Spring A (50.0 N/m) is attached to the ceiling. The top of spring B (30.0 N/m) is hooked onto the bottom of spring A. Then a 0.250-kg mass is then attached to the bottom of Spring B. (a) How far will the object fall until it reaches equilibrium (b) What is the period of the resulting oscillation
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