Now Concentrate on the Resultant Wave Shown in Blue

July 04, 2022 Post a Comment

Problem 27

Waves at Boundaries Which of the following wave characteristics remain unchanged when a wave crosses a boundary into a different medium: frequency, amplitude, wavelength, velocity, and/or direction?

Mayukh B.

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Problem 28

Refraction of Waves Notice in Figure $14-17$ a how the wave changes direction as it passes from one medium to another. Can two-dimensional waves cross a boundary between two media without changing direction? Explain.

Mayukh B.

Numerade Educator

Problem 29

Standing Waves In a standing wave on a string fixed at both ends, how is the number of nodes related to the number of antinodes?

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Problem 30

Critical Thinking As another way to understand wave reflection, cover the right-hand side of each drawing in Figure $14-13$ a with a piece of paper. The edge of the paper should be at point $N$, the node. Now, concentrate on the resultant wave, shown in darker blue. Note that it acts like a wave reflected from a boundary. Is the boundary a rigid wall, or is it open-ended? Repeat this exercise for Figure $14-13 \mathrm{b}$

Mayukh B.

Numerade Educator

Problem 31

Complete the concept map using the following terms and symbols: amplitude, frequency, $v, \lambda, T$ (FIGURE CANNOT COPY)

Mayukh B.

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Problem 32

What is periodic motion? Give three examples of periodic motion. (14.1)

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Problem 33

What is the difference between frequency and period? How are they related?

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Problem 34

What is simple harmonic motion? Give an example of simple harmonic motion. (14.1)

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Problem 35

If a spring obeys Hooke's law, how does it behave? (14.1)

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Problem 36

How can the spring constant of a spring be determined from a graph of force versus displacement? (14.1)

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Problem 37

How can the potential energy in a spring be determined from the graph of force versus displacement? (14.1)

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Problem 38

Does the period of a pendulum depend on the mass of the bob? The length of the string? Upon what else does the period depend? (14.1)

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Problem 39

What conditions are necessary for resonance to occur? (14.1)

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Problem 40

How many general methods of energy transfer are there? Give two examples of each. (14.2)

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Problem 41

What is the primary difference between a mechanical wave and an electromagnetic wave? (14.2)

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Problem 42

What are the differences among transverse, longitudinal, and surface waves?

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Problem 43

Waves are sent along a spring of fixed length. (14.2)
a. Can the speed of the waves in the spring be changed? Explain.
b. Can the frequency of a wave in the spring be changed? Explain.

Mayukh B.

Numerade Educator

Problem 44

What is the wavelength of a wave? (14.2)

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Problem 45

Suppose you send a pulse along a rope. How does the position of a point on the rope before the pulse arrives compare to the point's position after the pulse has passed? (14.2)

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Problem 46

What is the difference between a wave pulse and a periodic wave? (14.2)

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Problem 47

Describe the difference between wave frequency and wave velocity. (14.2)

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Problem 48

Suppose you produce a transverse wave by shaking one end of a spring from side to side. How does the frequency of your hand compare with the frequency of the wave?

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Problem 49

When are points on a wave in phase with each other? When are they out of phase? Give an example of each. (14.2)

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Problem 50

What is the amplitude of a wave and what does it represent? (14.2)

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Problem 51

Describe the relationship between the amplitude of a wave and the energy it carries. (14.2)

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Problem 52

When a wave reaches the boundary of a new medium, what happens to it?

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Problem 53

When a wave crosses a boundary between a thin and a thick rope, as shown in Figure $14-18$, its wavelength and speed change, but its frequency does not. Explain why the frequency is constant. (14.3) (FIGURE CANNOT COPY)

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Numerade Educator

Problem 54

How does a spring pulse reflected from a rigid wall differ from the incident pulse? (14.3)

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Problem 55

Describe interference. Is interference a property of only some types of waves or all types of waves?

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Problem 56

What happens to a spring at the nodes of a standing wave? (14.3)

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Problem 57

Violins A metal plate is held fixed in the center and sprinkled with sugar. With a violin bow, the plate is stroked along one edge and made to vibrate. The sugar begins to collect in certain areas and move away from others. Describe these regions in terms of standing waves. (14.3)

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Numerade Educator

Problem 58

If a string is vibrating in four parts, there are points where it can be touched without disturbing its motion. Explain. How many of these points exist? (14.3)

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Problem 59

Wave fronts pass at an angle from one medium into a second medium, where they travel with a different speed. Describe two changes in the wave fronts. What does not change? (14.3)

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Problem 60

A ball bounces up and down on the end of a spring. Describe the energy changes that take place during one complete cycle. Does the total mechanical energy change?

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Problem 61

Can a pendulum clock be used in the orbiting International Space Station? Explain.

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Numerade Educator

Problem 62

Suppose you hold a $1-\mathrm{m}$ metal bar in your hand and hit its end with a hammer, first, in a direction parallel to its length, and second, in a direction at right angles to its length. Describe the waves produced in the two cases.

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Problem 63

Suppose you repeatedly dip your finger into a sink full of water to make circular waves. What happens to the wavelength as you move your finger faster?

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Problem 64

What happens to the period of a wave as the frequency increases?

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Problem 65

What happens to the wavelength of a wave as the frequency increases?

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Problem 66

Suppose you make a single pulse on a stretched spring. How much energy is required to make a pulse with twice the amplitude?

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Problem 67

You can make water slosh back and forth in a shallow pan only if you shake the pan with the correct frequency. Explain.

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Problem 68

In each of the four waves in Figure $14-19$, the pulse on the left is the original pulse moving toward the right. The center pulse is a reflected pulse; the pulse on the right is a transmitted pulse. Describe the rigidity of the boundaries at $A, B, C,$ and $D$ (FIGURES CANNOT COPY)

Mayukh B.

Numerade Educator

Problem 69

A spring stretches by $0.12 \mathrm{m}$ when some apples weighing $3.2 \mathrm{N}$ are suspended from it, as shown in Figure $14-20 .$ What is the spring constant of the spring? (FIGURE CANNOT COPY)

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Problem 70

Car Shocks Each of the coil springs of a car has a spring constant of $25,000 \mathrm{N} / \mathrm{m}$. How much is each spring compressed if it supports one-fourth of the car's $12,000-\mathrm{N}$ weight?

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Problem 71

How much potential energy is stored in a spring with a spring constant of $27 \mathrm{N} / \mathrm{m}$ if it is stretched by $16 \mathrm{cm} ?$

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Problem 72

Rocket Launcher A toy rocket-launcher contains a spring with a spring constant of $35 \mathrm{N} / \mathrm{m}$. How far must the spring be compressed to store $1.5 \mathrm{J}$ of energy?

Mayukh B.

Numerade Educator

Problem 73

Force-versus-length data for a spring are plotted on the graph in Figure $14-21$
a. What is the spring constant of the spring?
b. What is the energy stored in the spring when it is stretched to a length of $0.50 \mathrm{m} ?$ (GRAPH CANNOT COPY)

Mayukh B.

Numerade Educator

Problem 74

How long must a pendulum be to have a period of 2.3 s on the Moon, where $g=1.6 \mathrm{m} / \mathrm{s}^{2} ?$

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Problem 75

Building Motion The Sears Tower in Chicago, shown in Figure $14-22,$ sways back and forth in the wind with a frequency of about $0.12 \mathrm{Hz}$. What is its period of vibration? (IMAGE CAMMOT COPY)

Mayukh B.

Numerade Educator

Problem 76

Ocean Waves An ocean wave has a length of $12.0 \mathrm{m} .$ A wave passes a fixed location every $3.0 \mathrm{s}$ What is the speed of the wave?

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Problem 77

Water waves in a shallow dish are 6.0 -cm long. At one point, the water moves up and down at a rate of 4.8 oscillations/s.
a. What is the speed of the water waves?
b. What is the period of the water waves?

Mayukh B.

Numerade Educator

Problem 78

Water waves in a lake travel $3.4 \mathrm{m}$ in 1.8 s. The period of oscillation is $1.1 \mathrm{s}$
a. What is the speed of the water waves?
b. What is their wavelength?

Mayukh B.

Numerade Educator

Problem 79

Sonar A sonar signal of frequency $1.00 \times 10^{6} \mathrm{Hz}$ has a wavelength of $1.50 \mathrm{mm}$ in water.
a. What is the speed of the signal in water?
b. What is its period in water?
c. What is its period in air?

Mayukh B.

Numerade Educator

Problem 80

A sound wave of wavelength $0.60 \mathrm{m}$ and a velocity of $330 \mathrm{m} / \mathrm{s}$ is produced for $0.50 \mathrm{s}$
a. What is the frequency of the wave?
b. How many complete waves are emitted in this time interval?
c. After $0.50 \mathrm{s}$, how far is the front of the wave from the source of the sound?

Mayukh B.

Numerade Educator

Problem 81

The speed of sound in water is $1498 \mathrm{m} / \mathrm{s}$. A sonar signal is sent straight down from a ship at a point just below the water surface, and 1.80 s later, the reflected signal is detected. How deep is the water?

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Problem 82

Pepe and Alfredo are resting on an offshore raft after a swim. They estimate that 3.0 m separates a trough and an adjacent crest of each surface wave on the lake. They count 12 crests that pass by the raft in $20.0 \mathrm{s} .$ Calculate how fast the waves are moving.

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Numerade Educator

Problem 83

Earthquakes The velocity of the transverse waves produced by an earthquake is $8.9 \mathrm{km} / \mathrm{s},$ and that of the longitudinal waves is $5.1 \mathrm{km} / \mathrm{s} .$ A seismograph records the arrival of the transverse waves $68 \mathrm{s}$ before the arrival of the longitudinal waves. How far away is the earthquake?

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Problem 84

Sketch the result for each of the three cases shown in Figure $14-23,$ when the centers of the two approaching wave pulses lie on the dashed line so that the pulses exactly overlap. (FIGURE CANNOT COPY)

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Problem 85

If you slosh the water in a bathtub at the correct frequency, the water rises first at one end and then at the other. Suppose you can make a standing wave in a 150 -cm-long tub with a frequency of $0.30 \mathrm{Hz}$. What is the velocity of the water wave?

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Problem 86

Guitars The wave speed in a guitar string is $265 \mathrm{m} / \mathrm{s}$ The length of the string is $63 \mathrm{cm} .$ You pluck the center of the string by pulling it up and letting go. Pulses move in both directions and are reflected off the ends of the string,
a. How long does it take for the pulse to move to the string end and return to the center?
b. When the pulses return, is the string above or below its resting location?
c. If you plucked the string $15 \mathrm{cm}$ from one end of the string, where would the two pulses meet?

Mayukh B.

Numerade Educator

Problem 87

Sketch the result for each of the four cases shown in Figure $14-24,$ when the centers of each of the two wave pulses lie on the dashed line so that the pulses exactly overlap. (FIGURE CANNOT COPY)

Mayukh B.

Numerade Educator

Problem 88

What is the period of a pendulum with a length of $1.4 \mathrm{m} ?$

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Numerade Educator

Problem 89

The frequency of yellow light is $5.1 \times 10^{14} \mathrm{Hz}$. Find the wavelength of yellow light. The speed of light is $3.00 \times 10^{8} \mathrm{m} / \mathrm{s}$

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Numerade Educator

Problem 90

Radio Wave AM-radio signals are broadcast at frequencies between $550 \mathrm{kHz}$ (kilohertz) and $1600 \mathrm{kHz}$ and travel $3.0 \times 10^{8} \mathrm{m} / \mathrm{s}$
a. What is the range of wavelengths for these signals?
b. FM frequencies range between $88 \mathrm{MHz}$ (megahertz) and $108 \mathrm{MHz}$ and travel at the same speed. What is the range of FM wavelengths?

Mayukh B.

Numerade Educator

Problem 91

You are floating just offshore at the beach. Even though the waves are steadily moving in toward the beach, you don't move any closer to the beach.
a. What type of wave are you experiencing as you float in the water?
b. Explain why the energy in the wave does not move you closer to shore.
c. In the course of 15 s you count ten waves that pass you. What is the period of the waves?
d. What is the frequency of the waves?
e. You estimate that the wave crests are 3 m apart. What is the velocity of the waves?
f. After returning to the beach, you learn that the waves are moving at $1.8 \mathrm{m} / \mathrm{s}$. What is the actual wavelength of the waves?

Mayukh B.

Numerade Educator

Problem 92

Bungee Jumper A high-altitude bungee jumper jumps from a hot-air balloon using a 540 -m-bungee cord. When the jump is complete and the jumper is just suspended from the cord, it is stretched 1710 m. What is the spring constant of the bungee cord if the jumper has a mass of $68 \mathrm{kg} ?$

Mayukh B.

Numerade Educator

Problem 93

The time needed for a water wave to change from the equilibrium level to the crest is $0.18 \mathrm{s}$
a. What fraction of a wavelength is this?
b. What is the period of the wave?
c. What is the frequency of the wave?

Mayukh B.

Numerade Educator

Problem 94

When a 225 -g mass is hung from a spring, the spring stretches $9.4 \mathrm{cm} .$ The spring and mass then are pulled $8.0 \mathrm{cm}$ from this new equilibrium position and released. Find the spring constant of the spring and the maximum speed of the mass.

Mayukh B.

Numerade Educator

Problem 95

Amusement Ride You notice that your favorite amusement-park ride seems bigger. The ride consists of a carriage that is attached to a structure so it swings like a pendulum. You remember that the carriage used to swing from one position to another and back again eight times in exactly 1 min. Now it only swings six times in 1 min. Give your answers to the following questions to two significant digits.
a. What was the original period of the ride?
b. What is the new period of the ride?
c. What is the new frequency?
d. How much longer is the arm supporting the carriage on the larger ride?
E. If the park owners wanted to double the period of the ride, what percentage increase would need to be made to the length of the pendulum?

Mayukh B.

Numerade Educator

Problem 96

Clocks The speed at which a grandfather clock runs is controlled by a swinging pendulum.
a. If you find that the clock loses time each day, what adjustment would you need to make to the pendulum so it will keep better time?
b. If the pendulum currently is $15.0 \mathrm{cm},$ by how much would you need to change the length to make the period lessen by $0.0400 \mathrm{s} ?$

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Numerade Educator

Problem 97

Bridge Swinging In the summer over the New River in West Virginia, several teens swing from bridges with ropes, then drop into the river after a few swings back and forth.
a. If Pam is using a 10.0 -m length of rope, how long will it take her to reach the peak of her swing at the other end of the bridge?
b. If Mike has a mass that is 20 kg more than Pam, how would you expect the period of his swing to differ from Pam's?
c. At what point in the swing is $K E$ at a maximum?
d. At what point in the swing is $P E$ at a maximum?
e. At what point in the swing is $K E$ at a minimum?
f. At what point in the swing is $P E$ at a minimum?

Mayukh B.

Numerade Educator

Problem 98

You have a mechanical fish scale that is made with
a spring that compresses when weight is added to
a hook attached below the scale. Unfortunately, the calibrations have completely worn off of the scale. However, you have one known mass of $500.0 \mathrm{g}$ that displaces the spring $2.0 \mathrm{cm} .$
a. What is the spring constant for the spring?
b. If a fish displaces the spring $4.5 \mathrm{cm},$ what is the mass of the fish?

Mayukh B.

Numerade Educator

Problem 99

Mayukh B.

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Problem 100

The velocity of a wave on a string depends on how tightly the string is stretched, and on the mass per unit length of the string. If $F_{T}$ is the tension in the string, and $\mu$ is the mass/unit length, then the velocity, $v,$ can be determined by the following equation. $$v=\sqrt{\frac{F_{\mathrm{T}}}{\mu}}$$
A piece of string 5.30 -m long has a mass of $15.0 \mathrm{g}$ What must the tension in the string be to make the wavelength of a $125-\mathrm{Hz}$ wave $120.0 \mathrm{cm} ?$

Mayukh B.

Numerade Educator

Problem 101

Analyze and Conclude A $20-\mathrm{N}$ force is required to stretch a spring by $0.5 \mathrm{m}$
a. What is the spring constant?
b. How much energy is stored in the spring?
c. Why isn't the work done to stretch the spring equal to the force times the distance, or $10 \mathrm{J} ?$

Mayukh B.

Numerade Educator

Problem 102

Make and Use Graphs Several weights were suspended from a spring and the resulting extensions of the spring were measured. Table 1 shows the collected data. (TABLE CANNOT COPY)
a. Make a graph of the force applied to the spring versus the spring length. Plot the force on the $y$ -axis.
b. Determine the spring constant from the graph.
c. Using the graph, find the elastic potential energy stored in the spring when it is stretched
to $0.50 \mathrm{m}$

Mayukh B.

Numerade Educator

Problem 103

Apply Concepts Gravel roads often develop regularly spaced ridges that are perpendicular to the road, as shown in Figure $14-25 .$ This effect, called washboarding, occurs because most cars travel at about the same speed and the springs that connect the wheels to the cars oscillate at about the same frequency. If the ridges on a road are $1.5 \mathrm{m}$ apart and cars travel on it at about $5 \mathrm{m} / \mathrm{s}$ what is the frequency of the springs' oscillation? (IMAGE CAMMOT COPY)

Mayukh B.

Numerade Educator

Problem 104

Research Christiaan Huygens' work on waves and the controversy between him and Newton over the nature of light. Compare and contrast their explanations of such phenomena as reflection and refraction. Whose model would you choose as the best explanation? Explain why.

Problem 105

A 1400 -kg drag racer automobile can complete a one-quarter mile $(402 \mathrm{m})$ course in $9.8 \mathrm{s}$. The final speed of the automobile is $250 \mathrm{mi} / \mathrm{h}(112 \mathrm{m} / \mathrm{s})$
(Chapter 11 )
a. What is the kinetic energy of the automobile?
b. What is the minimum amount of work that was done by its engine? Why can't you calculate the total amount of work done?
c. What was the average acceleration of the automobile?

Mayukh B.

Numerade Educator