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Exam 13: Vibrations and Waves

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Question 31

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What is the velocity of propagation if a wave has a frequency of 12. Hz and a wavelength of 3.0 m?

A) 28 m/s
B) 4.0 m/s
C) 6.0 m/s
D) 0.25 m/s
E) 36 m/s

F) A) and B)
G) C) and D)

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Question 32

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Spock has landed on a newly discovered planet and is instructed to determine its gravitational strength. He constructs a simple pendulum with a length of 700. mm and observes 20. full swings in 1 minute and 16.7 seconds. What does he deduce the "acceleration of gravity" to be from this?

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Question 33

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How would you "weigh" the astronauts in orbit (where they feel weightless) so that you can keep them in good health?

Simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?

When the speed of a wave depends on the wavelength (or frequency), the waves are said to exhibit diffraction.

Why can longitudinal earthquake waves go straight through the center of the Earth but transverse waves cannot?

Suppose you want to set up a simple pendulum with a period of 0.250 s. (a) What length is required if g = 9.80 m/s² on Earth? (b) What length would be required on the moon assuming g is 6 (assume exact) times LESS than on Earth?

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 velocity of waves. (d) Determine the fundamental frequency of this string.

A 0.30 kg mass is suspended on a string. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. (a) Write down its equation of motion. (b) Calculate the velocity of the mass at T/3 s.

Tarzan swings back and forth on a long vine. His friend Jane notices 30. swings in 2.4 minutes. (a) The frequency of the swing is ________. (b) The vine length is ________ meters.

Increasing the spring constant k of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the system's mass m.)

Consider the wave shown in Figure 13-5 below for the following item(s) . -The wavelength in Figure 13-5

A mass is attached to a spring. It oscillates at a frequency of 4.0 Hz when displaced a distance of 2.0 cm from equilibrium and released. What is the maximum velocity attained by the mass?

What mass should be attached to a vertical spring (k = 39.5 N/m) so that the natural vibration frequency of the system will be 1.00 Hz?

Compare two vibrating strings, each has the same tension, but the second has four times the mass density of the first. The wave speed along the 2nd string is how many times the speed along the 1st?

A 2.0 kg mass is attached to the end of a horizontal spring (k = 50. N/m) and set into simple harmonic motion with an amplitude of 10. cm. What is the total mechanical energy of this system?

Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?

Doubling only the amplitude of a vibrating mass-on-a-spring system produces what effect on the system frequency?

A string fixed at both ends is vibrating in its 8th harmonic. (a) How many nodes are on the string? (b) The 8th harmonic wavelength is what fraction of the string length? (c) If the 8th harmonic frequency is 976. Hz, what is the frequency of the 2nd overtone?

The mass of a mass-and-spring system is displaced 10 cm from its equilibrium position and released. A frequency of 4 Hz is observed. What frequency would be observed if the mass had been displaced only 5 cm and then released?