Conceptual Physics

Paul G. Hewitt

Chapter 19

Vibrations and Waves

Educators


Problem 1

What is a wiggle in time called? What do you call a wiggle in space and time?

Averell H.
Carnegie Mellon University

Problem 2

What is the source of all waves?

Shital R.
Numerade Educator

Problem 3

What is meant by the period of a pendulum?

Averell H.
Carnegie Mellon University

Problem 4

What is simple harmonic motion? Mention suitable examples.

Shital R.
Numerade Educator

Problem 5

How does a sine curve relate to the wave description?

Averell H.
Carnegie Mellon University

Problem 6

List some important differences between sound waves and light waves.

Shital R.
Numerade Educator

Problem 7

How many vibrations per second are represented in a radio wave of 101.7 MHz?

Averell H.
Carnegie Mellon University

Problem 8

How do frequency and period relate to each other?

Shital R.
Numerade Educator

Problem 9

In one word, what is it that moves from source to receiver in wave motion?

Averell H.
Carnegie Mellon University

Problem 10

Does the medium in which a wave travels move with the wave?

Shital R.
Numerade Educator

Problem 11

In what direction are the vibrations relative to the direction of wave travel in a transverse wave?

Averell H.
Carnegie Mellon University

Problem 12

In what direction are the vibrations relative to the direction of wave travel in a longitudinal wave?

Shital R.
Numerade Educator

Problem 13

The wavelength of a transverse wave is the distance between successive crests (or troughs). What is the wave-length of a longitudinal wave?

Averell H.
Carnegie Mellon University

Problem 14

What is the relationship between the velocity and the acceleration of a particle undergoing simple harmonic motion?

Shital R.
Numerade Educator

Problem 15

What is the superposition principle?

Averell H.
Carnegie Mellon University

Problem 16

What is meant by phase velocity and group velocity?

Shital R.
Numerade Educator

Problem 17

What kinds of waves can show interference?

Averell H.
Carnegie Mellon University

Problem 18

What is a node? What is an antinode?

Shital R.
Numerade Educator

Problem 19

Can standing waves be formed of transverse waves, longitudinal waves, or both?

Averell H.
Carnegie Mellon University

Problem 20

In the Doppler effect, does frequency change? Does wave speed change?

Shital R.
Numerade Educator

Problem 21

Can the Doppler effect be observed with longitudinal waves, with transverse waves, or with both?

Averell H.
Carnegie Mellon University

Problem 22

What is meant by a blue shift and a red shift for light?

Shital R.
Numerade Educator

Problem 23

How fast must a bug swim to keep up with the waves it produces? How fast must it move to produce a bow wave?

Averell H.
Carnegie Mellon University

Problem 24

How fast does a supersonic aircraft fly compared with the speed of sound?

Shital R.
Numerade Educator

Problem 25

How does the V shape of a bow wave depend on the speed of the source?

Averell H.
Carnegie Mellon University

Problem 26

A bow wave on the surface of water is two-dimensional. How about a shock wave in air?

Shital R.
Numerade Educator

Problem 27

True or false: A sonic boom occurs only when an aircraft is breaking through the sound barrier. Defend your answer.

Averell H.
Carnegie Mellon University

Problem 28

True or false: In order for an object to produce a sonic boom, it must be “noisy.” Give two examples to support your answer.

Shital R.
Numerade Educator

Problem 29

Tie a rubber tube, a spring, or a rope to a fixed support and produce standing waves. See how many nodes you can produce.

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Problem 30

Wet your finger and rub it slowly around the rim of a thin-rimmed, stemmed wine glass while you hold the base of the glass firmly to a tabletop with your other hand. The friction of your finger will excite standing waves in the glass, much like the wave made on the strings of a violin by the friction from a violin bow. Try it with a metal bowl.

Shital R.
Numerade Educator

Problem 31

Write a letter to Grandma and tell her how waves can cancel one another. Then describe what some of the applications of this physical phenomenon are these days.

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Problem 32

Frequency $=\frac{1}{\text { period }} ; f=1 / T$
What is the frequency, in hertz, that corresponds to each of the following periods: (a) 0.10 s, (b) 5 s, (c) 1$/ 60$ s?

Shital R.
Numerade Educator

Problem 33

Period $=\frac{1}{\text { frequency }} ; T=1 / f$
What is the period, in seconds, that corresponds to each of the following frequencies: (a) $10 \mathrm{H} z,(\mathrm{b}) 0.2 \mathrm{Hz},(\mathrm{c}) 60 \mathrm{Hz}$ ?

Averell H.
Carnegie Mellon University

Problem 34

Wave speed = $\frac{\text { wavelength }}{\text { period }}$ or frequency $\times$ wavelength;
$$v=f \lambda$$
What is the speed of a water wave of frequency 2 $\mathrm{Hz}$ and wavelength 1.5 $\mathrm{m}$ ?

Shital R.
Numerade Educator

Problem 35

Wave speed = $\frac{\text { wavelength }}{\text { period }}$ or frequency $\times$ wavelength;
$$v=f \lambda$$

How fast does a 200-Hz sound wave with a wavelength of 1.7 m travel?

Averell H.
Carnegie Mellon University

Problem 36

A radar transmitter sends a signal at the speed of light $\left(3 \times 10^{8} \mathrm{m} / \mathrm{s}\right)$ to an aeroplane 100 $\mathrm{km}$ away. After how much time will the signal be received back from the aeroplane?

Shital R.
Numerade Educator

Problem 37

A pendulum is constructed from a light string of length $l=100 \mathrm{cm}$ and a heavy mass $m=100 \mathrm{kg}$ . What is the period of the pendulum for small displacements?

Averell H.
Carnegie Mellon University

Problem 38

A mosquito flaps its wings 600 vibrations per second, which produces the annoying $600-\mathrm{Hz}$ buzz. Given that the speed of sound is 340 $\mathrm{m} / \mathrm{s}$ , how far does the sound travel between wing beats? In other words, find the wave-length of the mosquito's sound.

Shital R.
Numerade Educator

Problem 39

On a keyboard, you strike middle $C,$ whose frequency is 256 $\mathrm{Hz}$ .
(a) What is the period of one vibration of this tone?
(b) As the sound leaves the instrument at a speed of 340 $\mathrm{m} / \mathrm{s}$ , what is its wavelength in air?

Averell H.
Carnegie Mellon University

Problem 40

As shown in the drawing, the half-angle of the shock wave cone generated by a supersonic airplane is $45^{\circ} .$ What is the speed of the plane relative to the speed of sound?

Shital R.
Numerade Educator

Problem 41

An astronaut on the Moon attaches a small brass ball to a 1.00 -m length of string and makes a simple pendulum. She times 15 complete swings in 75 seconds. From this measurement she calculates the acceleration due to gravity on the Moon. What is her result?

Averell H.
Carnegie Mellon University

Problem 42

All the waves shown have the same speed in the same medium. Use a ruler and rank these waves from most to least for
(a) amplitude,
(b) wavelength,
(c) frequency, and
(d) period.

Shital R.
Numerade Educator

Problem 43

Shown here are four different pairs of transverse wave pulses that move toward each other. At some point in time, the pulses meet and interact (interfere) with each other. Rank the four cases, from most to least, on the

Averell H.
Carnegie Mellon University

Problem 44

Rank the pitches heard from the siren of a fire engine, from highest to lowest, when the fire engine is traveling
(a) toward the listener at 30 $\mathrm{km} / \mathrm{h}$ .
(b) toward the listener at 50 $\mathrm{km} / \mathrm{h}$ .
(c) away from the listener at 20 $\mathrm{km} / \mathrm{h}$ .

Shital R.
Numerade Educator

Problem 45

The shock waves $A, B,$ and $C$ are produced by supersonic aircraft. Rank their speeds from highest to lowest.

Averell H.
Carnegie Mellon University

Problem 46

Does the period of a pendulum depend on the mass of the bob? On the length of the string?

Shital R.
Numerade Educator

Problem 47

If a pendulum is shortened, does its frequency increase or decrease? What about its period?

Averell H.
Carnegie Mellon University

Problem 48

A grandfather pendulum clock keeps perfect time. Then it is relocated to a summer home high in the mountains. Does it run faster, slower, or the same? Explain.

Shital R.
Numerade Educator

Problem 49

You pick up an empty briefcase and let it swing to and fro at its natural frequency. If the case were filled with books, would the natural frequency be lower than, higher than, or the same as before?

Averell H.
Carnegie Mellon University

Problem 50

Is the time required to swing to and fro (the period) on a playground swing longer or shorter when you stand rather than sit? Explain.

Shital R.
Numerade Educator

Problem 51

What happens to the period of a wave when the frequency decreases?

Averell H.
Carnegie Mellon University

Problem 52

What happens to the wavelength of a wave when the frequency decreases?

Shital R.
Numerade Educator

Problem 53

If the speed of a wave doubles while the frequency remains the same, what happens to the wavelength?

Averell H.
Carnegie Mellon University

Problem 54

If the speed of a wave doubles while the wavelength remains the same, what happens to the frequency?

Shital R.
Numerade Educator

Problem 55

The needle of a sewing machine moves up and down in simple harmonic motion. Its driving force comes from a rotating wheel that is powered by an electric motor. How do you suppose the period of the up-and-down needle compares with the period of the rotating wheel? Defend your answer.

Averell H.
Carnegie Mellon University

Problem 56

You use a vice to firmly clamp one end of a hacksaw blade. You twang the free end and it vibrates. If you do the same, but first place a wad of clay on the free end, how, if at all, will the frequency of the vibration differ? Would it make a difference if the wad of clay were stuck to the middle? Explain. (Why could this question have been asked back in Chapter 8?)

Shital R.
Numerade Educator

Problem 57

If you shake the end of a spring to produce a wave, how does the frequency of the wave compare with the frequency of your shaking hand? Does your answer depend on whether you’re producing a transverse wave or a longitudinal wave? Defend your answer.

Averell H.
Carnegie Mellon University

Problem 58

What kind of motion should you impart to the nozzle of a garden hose so that the resulting stream of water approximates a sine curve?

Shital R.
Numerade Educator

Problem 59

What kind of motion should you impart to a stretched coiled spring (or Slinky) to provide a
(a) transverse wave?
(b) longitudinal wave?

Averell H.
Carnegie Mellon University

Problem 60

What kind of wave is each of the following?
(a) The sound of one whale calling another whale under water.
(b) A pulse sent down a stretched rope by snapping one end of it.
(c) The vibrations in a guitar string.

Shital R.
Numerade Educator

Problem 61

Red light has a longer wavelength than violet light. Which has the higher frequency?

Averell H.
Carnegie Mellon University

Problem 62

If we double the frequency of a vibrating object or the wave it produces, what happens to the period?

Shital R.
Numerade Educator

Problem 63

What is the frequency of the second hand of a clock? The minute hand? The hour hand?

Averell H.
Carnegie Mellon University

Problem 64

If you dip your finger repeatedly into a puddle of water, it creates waves. What happens to the wavelength if you dip your finger more frequently?

Shital R.
Numerade Educator

Problem 65

How does the frequency of vibration of a small object floating in water compare with the number of waves passing it each second?

Averell H.
Carnegie Mellon University

Problem 66

In terms of wavelength, show how far a wave travels in one period.

Shital R.
Numerade Educator

Problem 67

What is the source of mechanical waves? Of electromagnetic waves?

Averell H.
Carnegie Mellon University

Problem 68

How many nodes, not including the endpoints, are there in a standing wave that is two wavelengths long? Three wavelengths long?

Shital R.
Numerade Educator

Problem 69

A rock is dropped in water, and waves spread over the flat surface of the water. What becomes of the energy in these waves when they die out?

Averell H.
Carnegie Mellon University

Problem 70

The wave patterns seen in Figures 19.4 and 19.8 are composed of circles. What does this tell you about the speed of waves moving in different directions?

Shital R.
Numerade Educator

Problem 71

Why is lightning seen before thunder is heard?

Averell H.
Carnegie Mellon University

Problem 72

A banjo player plucks the middle of a string pinned down at both ends. Where are the nodes of the standing wave in the string? What is the wavelength of the vibrating string?

Shital R.
Numerade Educator

Problem 73

Violinists sometimes bow a string to produce maximum vibration (antinodes) at one-quarter and three-quarters of the string length rather than at the middle of the string. Then the string vibrates with a wavelength equal to the string length rather than twice the string length. (See Figure 19.13a and b.) What is the effect on the frequency when this occurs?

Averell H.
Carnegie Mellon University

Problem 74

A bat chirps as it flies toward a wall. Is the frequency of the echoed chirps it receives higher than, lower than, or the same as the emitted ones?

Shital R.
Numerade Educator

Problem 75

A railroad locomotive is at rest with its whistle shrieking, then starts moving toward you.
(a) Does the frequency of sound that you hear increase, decrease, or stay the same?
(b) How about the wavelength reaching your ear?
(c) How about the speed of sound in the air between you and the locomotive?

Averell H.
Carnegie Mellon University

Problem 76

Why is there a Doppler effect when the source of the sound is stationary and the listener is in motion? In
which direction should the listener move to hear a higher frequency? A lower frequency?

Shital R.
Numerade Educator

Problem 77

When you blow your horn while driving toward a stationary listener, the listener hears an increase in the frequency of the horn. Would the listener hear an increase in the horn frequency if he or she were also in a car traveling at the same speed in the same direction as you are? Explain.

Averell H.
Carnegie Mellon University

Problem 78

Is there an appreciable Doppler effect when the motion of the source is at right angles to a listener? Explain.

Shital R.
Numerade Educator

Problem 79

How does the Doppler effect aid police in detecting speeding motorists?

Averell H.
Carnegie Mellon University

Problem 80

Would it be correct to say that the Doppler effect is the apparent change in the speed of a wave due to motion of the source? (Why is this question a test of reading comprehension as well as a test of physics knowledge?)

Shital R.
Numerade Educator

Problem 81

How does the phenomenon of interference play a role in the production of bow waves or shock waves?

Averell H.
Carnegie Mellon University

Problem 82

What can you say about the speed of a boat that makes a bow wave?

Shital R.
Numerade Educator

Problem 83

Does a sonic boom occur at the moment when an aircraft exceeds the speed of sound? Explain.

Averell H.
Carnegie Mellon University

Problem 84

Why is it that a subsonic aircraft, no matter how loud it may be, cannot produce a sonic boom?

Shital R.
Numerade Educator

Problem 85

Imagine a superfast fish that is able to swim faster than the speed of sound in water. Would such a fish produce a “sonic boom”?

Averell H.
Carnegie Mellon University

Problem 86

Make up a multiple-choice question that would check a classmate’s understanding of the distinction between a transverse wave and a longitudinal wave.

Shital R.
Numerade Educator

Problem 87

Make up a multiple-choice question that would check a classmate’s understanding of any of the terms that describe a wave.

Averell H.
Carnegie Mellon University

Problem 88

A heavy person and a light person swing to and fro on swings of the same length. Discuss who has the longer period.

Shital R.
Numerade Educator

Problem 89

Does it make sense that the mass of a bob in a simple pendulum doesn’t affect the frequency of the pendulum? In your discussion cite whether or not mass affects the acceleration of free fall.

Averell H.
Carnegie Mellon University

Problem 90

If a gas tap is turned on for a few seconds, someone a couple of meters away will hear the gas escaping long before she smells it. What does this indicate about the speed of sound and the speed at which molecules diffuse through the sound-carrying medium?

Shital R.
Numerade Educator

Problem 91

Discuss how some learners confuse the two terms wave speed and wave frequency when they assume that the terms refer to the same thing.

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Problem 92

Astronomers find that light emitted by a particular element at one edge of the Sun has a slightly higher frequency than light from that element at the opposite edge. What do these measurements tell us about the Sun’s motion?

Shital R.
Numerade Educator

Problem 93

If the sound of an airplane does not come from the part of the sky where the plane is seen, discuss whether or not this implies that the airplane is traveling faster than the speed of sound.

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Problem 94

Does the conical angle of a shock wave open wider, narrow down, or remain constant as a supersonic aircraft increases its speed? Draw a sketch to make your point.

Shital R.
Numerade Educator