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Vibrations and Waves

1. A spring stretches by 25.0 cm when a
0.500-kg mass is suspended from its end.

  1. Determine the spring constant.

  2. How much elastic potential energy is stored in the spring when it is stretched this far?

2. A spring has a spring constant of 135 N/m. How far must it be compressed so that 4.39 J of elastic potential energy is stored in the spring?

3. On a planet where the gravitational field is five times g on Earth, a pendulum swings back and forth with a period of 1.22 s. What is the length of the pendulum?

4. Sonya hears water dripping from the eaves
of the house onto a porch roof. She counts
30 drops in 1.0 min.

  1. What is the frequency of the drops?

  2. What is the period of the drops?

5. Hiroshi is generating waves on a rope
by flipping the rope up and down. Each motion up or down lasts 0.20 s. The vertical distance from a crest to a trough is 0.40 m.

  1. What is the amplitude of the wave?

  2. What is the frequency of the waves?

6. A water wave travels a distance of 15 m
in 1 min. When this wave passes a point where a cork is floating in the water, it
causes the cork to move up and down
12 times in 15 s.

  1. What is the speed of this water wave?

  2. What is the wavelength of this water wave?

  3. What is the period of this water wave?

7. A Love wave—one of the four types of waves associated with earthquakes—is a transverse wave in which the surface of Earth moves back and forth as the wave passes. What is the speed of a Love wave that has a period of 150 s and a wavelength of 620 km?

8. A pulse with an amplitude of 0.53 m travels to the right along a rope. Another pulse, with an amplitude of 0.24 m, travels to the left along the same rope. The two pulses approach each other. What is the amplitude of the rope at the point where the midpoints of the pulses pass each other?

9. Part a of the figure below shows a pulse traveling at a speed of 1.0 m/s in a coil spring to which a second spring is attached at point A. Part b of the figure shows the springs a short time later.



  1. What is the amplitude of the incident pulse?

  2. What is the speed of the reflected pulse?

  3. What is the speed of the transmitted pulse?


Name _____________________________

Supplemental Problems

continued


10. A physics teacher attaches an electric oscillator to one end of a 2.0-m horizontal spring and attaches the other end of the spring to a stationary hook in the wall. She adjusts the frequency of the oscillator to produce a standing wave in the spring. Students observe that the standing wave has three nodes and two antinodes. She then doubles the frequency of the oscillations and produces another standing wave. How many nodes and antinodes do the students observe in the new standing wave?

11. What magnitude force will compress a spring so that the spring elastic potential increases by 0.24 J? The spring constant is 18 N/cm.

12. Each back-and-forth movement of the bob in a small pendulum clock releases a cog on a wheel. As the cog is released, the wheel undergoes a slight rotation. If the release of three cogs moves the second hand of the clock forward 1.0 s, what is the length of the pendulum?

13. Calculate the frequency in hertz of each of the following:

  1. a “new” moon (period  27.3 days)

  2. a day on Earth

  3. a breath (Assume a breathing rate of 812 breaths in 60.0 s.)

  4. a heart beat (Assume a heart rate of 1.01.6 beats per second.)

14. The distance between four consecutive antinodes of a standing wave in a spring is
42 cm. What is the wavelength of the standing wave? Hint: The distance between two consecutive antinodes in a standing wave represents 0.5 .




Vibrations and Waves

1. A spring stretches by 25.0 cm when a
0.500-kg mass is suspended from its end.

a. Determine the spring constant.



b. How much elastic potential energy is stored in the spring when it is stretched this far?



2. A spring has a spring constant of 135 N/m. How far must it be compressed so that 4.39 J of elastic potential energy is stored in the spring?



3. On a planet where the gravitational field is five times g on Earth, a pendulum swings back and forth with a period of 1.22 s. What is the length of the pendulum?



4. Sonya hears water dripping from the eaves of the house onto a porch roof. She counts 30 drops in 1.0 min.

a. What is the frequency of the drops?



b. What is the period of the drops?



5. Hiroshi is generating waves on a rope by flipping the rope up and down. Each motion up or down lasts 0.20 s. The vertical distance from a crest to a trough is 0.40 m.

a. What is the amplitude of the wave?



b. What is the frequency of the waves?





6. A water wave travels a distance of 15 m in
1 min. When this wave passes a point where a cork is floating in the water, it causes the cork to move up and down 12 times in 15 s.

a. What is the speed of this water wave?



b. What is the wavelength of this water wave?



c. What is the period of this water wave?



7. A Love wave—one of the four types of waves associated with earthquakes—is a transverse wave in which the surface of Earth moves back and forth as the wave passes. What is the speed of a Love wave that has a period of 150 s and a wavelength of 620 km?



8. A pulse with an amplitude of 0.53 m travels to the right along a rope. Another pulse, with an amplitude of 0.24 m, travels to the left along the same rope. The two pulses approach each other. What is the amplitude of the rope at the point where the midpoints of the pulses pass each other?



9. Part a of the figure below shows a pulse traveling at a speed of 1.0 m/s in a coil spring to which a second spring is attached at point A. Part b of the figure shows the springs a short time later.



a. What is the amplitude of the incident pulse?

0.10 m

b. What is the speed of the reflected pulse?

The reflected pulse and the incident pulse travel in the same spring, so they have the same speed of 1.0 m/s.

c. What is the speed of the transmitted pulse?







10. A physics teacher attaches an electric oscillator to one end of a 2.0-m horizontal spring and attaches the other end of the spring to a stationary hook in the wall. She adjusts the frequency of the oscillator to produce a standing wave in the spring. Students observe that the standing wave has three nodes and two antinodes. She then doubles the frequency of the oscillations and produces another standing wave. How many nodes and antinodes do the students observe in the new standing wave?

For f1, there are three nodes and two antinodes, indicating that the standing wave has a wavelength of 2.0 m, the same as the length of the spring.





The new standing wave has a wavelength of half the length of the spring. The spring contains two full wavelengths; therefore, the students observe five nodes and four antinodes.

11. What magnitude force will compress a spring so that the spring elastic potential increases by 0.24 J? The spring constant is
18 N/cm.





12. Each back-and-forth movement of the bob in a small pendulum clock releases a cog on a wheel. As the cog is released, the wheel undergoes a slight rotation. If the release of three cogs moves the second hand of the clock forward 1.0 s, what is the length of the pendulum?



13. Calculate the frequency in hertz of each of the following:

a. a “new” moon (period  27.3 days)



b. a day on Earth

It takes Earth 1.0 days to rotate on its axis, so the period is 1.0 days.



c. a breath (Assume a breathing rate of
8–12 breaths in 60.0 s.)



d. a heart beat (Assume a heart rate of
1.0–1.6 beats per second.)



14. The distance between four consecutive antin-odes of a standing wave in a spring is 42 cm. What is the wavelength of the standing wave? Hint: The distance between two consecutive antinodes in a standing wave represents 0.5 .

The distance between four antinodes represents 1.5 .



Chapter 14 Vibrations and Waves

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.




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