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Physics

Raymond A. Serway, Jerry S. Faughn

Chapter 11

Vibrations and Waves - all with Video Answers

Educators

Chapter Questions

02:28

Problem 1

What characterizes an object's motion as simple harmonic?

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07:05

Problem 2

List four examples of simple harmonic motion.

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04:48

Problem 3

Does the acceleration of a simple harmonic oscillator remain constant during its motion? Is the acceleration ever zero? Explain.

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01:58

Problem 4

A pendulum is released $40^{\circ}$ from its resting position. Is its motion simple harmonic?

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08:33

Problem 5

April is about to release the bob of a pendulum. Before she lets go, what sort of potential energy does the bob have? How does the energy of the bob change as it swings through one full cycle of motion?

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02:27

Problem 6

An ideal mass-spring system vibrating with simple harmonic motion would oscillate indefinitely. Explain why.

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04:47

Problem 7

In a simple pendulum, the weight of the bob can be divided into two components, one tangent to the bob's direction of motion and the other perpendicular to the bob's direction of motion. Which of these is the restoring force, and why?

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06:05

Problem 8

Janet wants to find the spring constant of a given spring, so she hangs the spring vertically and attaches a $0.40 \mathrm{kg}$ mass to the spring's other end. If the spring stretches $3.0 \mathrm{cm}$ from its equilibrium position, what is the spring constant?

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03:26

Problem 9

In preparing to shoot an arrow, an archer pulls a bowstring back $0.40 \mathrm{m}$ by exerting a force that increases uniformly from 0 to 230 N. What is the equivalent spring constant of the bow?

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03:06

Problem 10

A child swings on a playground swing. How many times does the child swing through the swing's equilibrium position during the course of a single period of motion?

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03:46

Problem 11

What is the total distance traveled by an object moving back and forth in simple harmonic motion in a time interval equal to its period when its amplitude is equal to $A ?$

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04:02

Problem 12

How is the period of a simple harmonic vibration related to its frequency?

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06:06

Problem 13

What happens to the period of a simple pendulum when the pendulum's length is doubled? What happens when the suspended mass is doubled?

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02:34

Problem 14

A pendulum bob is made with a ball filled with water. What would happen to the frequency of vibration of this pendulum if a hole in the ball allowed water to slowly leak out? (Treat the pendulum as a simple pendulum.)

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05:08

Problem 15

If a pendulum clock keeps perfect time at the base of a mountain, will it also keep perfect time when moved to the top of the mountain? Explain.

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02:42

Problem 16

If a grandfather clock is running slow, how can you adjust the length of the pendulum to correct the time?

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03:45

Problem 17

A simple pendulum can be used as an altimeter on a plane. How will the period of the pendulum vary as the plane rises from the ground to its final cruising altitude?

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02:25

Problem 18

Will the period of a vibrating mass-spring system on Earth be different from the period of an identical mass-spring system on the moon? Why or why not?

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03:52

Problem 19

Find the length of a pendulum that oscillates with a frequency of $0.16 \mathrm{Hz}$

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07:00

Problem 20

A pendulum that moves through its equilibrium position once every $1.000 \mathrm{s}$ is sometimes called a seconds pendulum.
a. What is the period of any seconds pendulum?
b. In Cambridge, England, a seconds pendulum is $0.9942 \mathrm{m}$ long. What is the free-fall acceleration in Cambridge?
c. In Tokyo, Japan, a seconds pendulum is $0.9927 \mathrm{m}$ long. What is the free-fall acceleration in Tokyo?

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04:56

Problem 21

A spring with a spring constant of $1.8 \times 10^{2} \mathrm{N} / \mathrm{m}$ is attached to a $1.5 \mathrm{kg}$ mass and then set in motion.
a. What is the period of the mass-spring system?
b. What is the frequency of the vibration?

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10:04

Problem 22

What is common to all waves?

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06:19

Problem 23

How do transverse and longitudinal waves differ?

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02:12

Problem 24

The figure below depicts a pulse wave traveling on a spring.
a. In which direction are the particles of the medium vibrating?
b. Is this wave transverse or longitudinal?

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02:12

Problem 25

In a stretched spring, several coils are pinched together and others are spread farther apart than usual. What sort of wave is this?

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09:20

Problem 26

How far does a wave travel in one period?

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03:02

Problem 27

If you shook the end of a rope up and down three times each second, what would be the period of the waves set up in the rope? What would be the frequency?

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03:44

Problem 28

Give three examples of mechanical waves. How are these different from electromagnetic waves, such as light waves?

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03:27

Problem 29

How does a single point on a string move as a transverse wave passes by that point?

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04:30

Problem 30

What happens to the wavelength of a wave on a string when the frequency is doubled? What happens to the speed of the wave?

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02:57

Problem 31

Why do sound waves need a medium through which to travel?

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01:05

Problem 32

Two tuning forks with frequencies of $256 \mathrm{Hz}$ and $512 \mathrm{Hz}$ are struck. Which of the sounds will move faster through the air?

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03:03

Problem 33

What is one advantage of transferring energy by electromagnetic waves? (FIGURE CAN'T COPY)

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05:50

Problem 34

A wave traveling in the positive $x$ direction with a frequency of $25.0 \mathrm{Hz}$ is shown in the figure above. Find the following values for this wave:
a. amplitude
b. wavelength
c. period
d. speed

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01:53

Problem 35

Microwaves travel at the speed of light, $3.00 \times 10^{8} \mathrm{m} / \mathrm{s}$ When the frequency of microwaves is $9.00 \times 10^{9} \mathrm{Hz}$ what is their wavelength?

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04:41

Problem 36

Using the superposition principle, draw the resultant waves for each of the examples below. (FIGURE CAN'T COPY)

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03:24

Problem 37

What is the difference between constructive interference and destructive interference?

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05:07

Problem 38

Which one of the waveforms shown below is the resultant waveform? (FIGURE CAN'T COPY)

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05:37

Problem 39

Anthony sends a series of pulses of amplitude $24 \mathrm{cm}$ down a string that is attached to a post at one end. Assuming the pulses are reflected with no loss of amplitude, what is the amplitude at a point on the string where two pulses are crossing if
a. the string is rigidly attached to the post?
b. the end at which reflection occurs is free to slide up and down?

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02:46

Problem 40

Can more than two waves interfere in a given medium?

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01:48

Problem 41

What is the resultant displacement at a position where destructive interference is complete?

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01:34

Problem 42

When two waves interfere, can the resultant wave be larger than either of the two original waves? If so, under what conditions?

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09:31

Problem 43

Which of the following wavelengths will produce standing waves on a string that is 3.5 m long?
a. $1.75 \mathrm{m}$
b. $3.5 \mathrm{m}$
c. $5.0 \mathrm{m}$
d. $7.0 \mathrm{m}$

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03:12

Problem 44

In an arcade game, a $0.12 \mathrm{kg}$ disk is shot across a frictionless horizontal surface by being compressed against a spring and then released. If the spring has a spring constant of $230 \mathrm{N} / \mathrm{m}$ and is compressed from its equilibrium position by $6.0 \mathrm{cm},$ what is the magnitude of the spring force on the disk at the moment it is released?

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02:50

Problem 45

A child's toy consists of a piece of plastic attached to a spring, as shown at right. The spring is compressed against the floor a distance of $2.0 \mathrm{cm}$ and released. If the spring constant is $85 \mathrm{N} / \mathrm{m},$ what is the magnitude of the spring force acting on the toy at the moment it is released?

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05:40

Problem 46

You dip your finger into a pan of water twice each second, producing waves with crests that are separated by $0.15 \mathrm{m} .$ Determine the frequency, period, and speed of these water waves.

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04:25

Problem 47

A sound wave traveling at $343 \mathrm{m} / \mathrm{s}$ is emitted by the foghorn of a tugboat. An echo is heard 2.60 s later. How far away is the reflecting object?

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03:33

Problem 48

The notes produced by a violin range in frequency from approximately $196 \mathrm{Hz}$ to $2637 \mathrm{Hz}$. Find the possible range of wavelengths in air produced by this instrument when the speed of sound in air is $340 \mathrm{m} / \mathrm{s}$

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02:28

Problem 49

What is the free-fall acceleration in a location where the period of a $0.850 \mathrm{m}$ long pendulum is $1.86 \mathrm{s} ?$

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02:35

Problem 50

Yellow light travels through a certain glass block at a speed of $1.97 \times 10^{8} \mathrm{m} / \mathrm{s} .$ The wavelength of the light in this particular type of glass is $3.81 \times 10^{-7} \mathrm{m}$ $(381 \mathrm{nm}) .$ What is the frequency of the yellow light?

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13:33

Problem 51

A certain pendulum clock that works perfectly on Earth is taken to the moon, where $a_{g}=1.63 \mathrm{m} / \mathrm{s}^{2} .$ If the clock is started at 12: 00 A.M., what will it read after $24.0 \mathrm{h}$ have passed on Earth?

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