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Exam 11: Oscillations and Waves

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Question 21

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A string of length 2.5 m is fixed at both ends. When the string vibrates at a frequency of 85 Hz, a standing wave with five loops is formed. (a) Determine the distance between two adjacent nodes. (b) Determine the wavelength of the waves that travel on the string. (c) Determine the speed of traveling waves on this string. (d) Determine the fundamental frequency of this string.

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(a) 0.50 m...

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Question 22

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A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing?

A) 6.00 s
B) 2.00 s
C) 3.46 s
D) 1.15 s
E) 0.667 s

F) D) and E)
G) None of the above

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Question 23

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One of the harmonics of a string fixed at both ends has a frequency of 52.2 Hz and the next higher harmonic has a frequency of 60.9 Hz. What is the fundamental frequency of the string?

What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is $8.60 \times 10 ^ { 3 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$

The density of aluminum is $2700 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ If transverse waves travel at 38 m/s in an aluminum wire of diameter 4.6 mm, what is the tension on the wire?

As shown in the figure, a 0.23-kg ball is suspended from a string 6.87 m long and is pulled slightly to the left. As the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant (force constant) is 19 N/m. (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

A string that is 2.0 meters long is fixed at both ends and tightened until the wave speed is 18 m/s. What is the frequency of the standing wave shown in the figure?

An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of Oscillation of the object?

A ball swinging at the end of a massless string, as shown in the figure, undergoes simple harmonic motion. At what point (or points) is the magnitude of the instantaneous acceleration of the ball the Greatest?

What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g.

If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?

Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B?

What is the frequency of the wave shown in the figure?

A geologist suspends a 0.30-kg stone on an ideal spring. In equilibrium the stone stretches the spring 2.0 cm downward. The stone is then pulled an additional distance of 1.0 cm down and released from rest. (a) Write down the equation for the vertical position y of the stone as a function of time t, using the cosine function. Take the origin at the equilibrium point of the stone, with the positive y direction upward. (b) How fast is the stone moving at a time equal to 1/3 of its period of motion?

The equation of motion of a particle undergoing simple harmonic motion in the y direction is At time t=0.60 s determine the particle's (a) position, (b) velocity, and (c) acceleration.

A string of length L is under tension, and the speed of a wave in the string is What will be the speed of a wave in the string if the length is increased to 2 L but with no change in the mass or tension?

If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

What is the frequency of a pressure wave of wavelength 2.5 m that is traveling at 1400 m/s?

A 2.0-kg block on a frictionless table is connected to two springs whose opposite ends are fixed to walls, as shown in the figure. The springs have force constants (spring constants) What is the oscillation angular frequency of the block if

Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes. (a) What is the frequency (in hertz) of Tarzan's swing? (b) How long is the vine he is using?