Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

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1 Chapter 20. Traveling Waves You may not realize it, but you are surrounded by waves. The waviness of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It s less apparent that sound and light are also waves. Chapter Goal: To learn the basic properties of traveling waves.

2 Chapter 20. Traveling Waves Topics: The Wave Model One-Dimensional Waves Sinusoidal Waves Waves in Two and Three Dimensions Sound and Light Power, Intensity, and Decibels The Doppler Effect

3 Chapter 20. Reading Quizzes

4 A graph showing wave displacement versus position at a specific instant of time is called a A. snapshot graph. B. history graph. C. bar graph. D. line graph. E. composite graph.

5 A graph showing wave displacement versus position at a specific instant of time is called a A. snapshot graph. B. history graph. C. bar graph. D. line graph. E. composite graph.

6 A graph showing wave displacement versus time at a specific point in space is called a A. snapshot graph. B. history graph. C. bar graph. D. line graph. E. composite graph.

7 A graph showing wave displacement versus time at a specific point in space is called a A. snapshot graph. B. history graph. C. bar graph. D. line graph. E. composite graph.

8 A wave front diagram shows A. the wavelengths of a wave. B. the crests of a wave. C. how the wave looks as it moves toward you. D. the forces acting on a string that s under tension. E. Wave front diagrams were not discussed in this chapter.

9 A wave front diagram shows A. the wavelengths of a wave. B. the crests of a wave. C. how the wave looks as it moves toward you. D. the forces acting on a string that s under tension. E. Wave front diagrams were not discussed in this chapter.

10 The waves analyzed in this chapter are A. string waves. B. sound and light waves. C. sound and water waves. D. string, sound, and light waves. E. string, water, sound, and light waves.

11 The waves analyzed in this chapter are A. string waves. B. sound and light waves. C. sound and water waves. D. string, sound, and light waves. E. string, water, sound, and light waves.

12 Chapter 20. Basic Content and Examples

13 Transverse and Longitudinal Waves

14 Transverse and Longitudinal Waves

15 Wave Speed The speed of transverse waves on a string stretched with tension T s is where µ is the string s mass-to-length ratio, also called the linear density.

16 EXAMPLE 20.1 The speed of a wave pulse QUESTION:

17 EXAMPLE 20.1 The speed of a wave pulse

18 EXAMPLE 20.1 The speed of a wave pulse

19 EXAMPLE 20.1 The speed of a wave pulse

20 EXAMPLE 20.1 The speed of a wave pulse

21 One-Dimensional Waves To understand waves we must deal with functions of two variables, position and time. A graph that shows the wave s displacement as a function of position at a single instant of time is called a snapshot graph. For a wave on a string, a snapshot graph is literally a picture of the wave at this instant. A graph that shows the wave s displacement as a function of time at a single position in space is called a history graph. It tells the history of that particular point in the medium.

22 EXAMPLE 20.2 Finding a history graph from a snapshot graph QUESTION:

23 EXAMPLE 20.2 Finding a history graph from a snapshot graph

24 EXAMPLE 20.2 Finding a history graph from a snapshot graph

25 EXAMPLE 20.2 Finding a history graph from a snapshot graph

26 EXAMPLE 20.2 Finding a history graph from a snapshot graph

27 Sinusoidal Waves A wave source that oscillates with simple harmonic motion (SHM) generates a sinusoidal wave. The frequency f of the wave is the frequency of the oscillating source. The period T is related to the wave frequency f by The amplitude A of the wave is the maximum value of the displacement. The crests of the wave have displacement D crest = A and the troughs have displacement D trough = A.

28 Sinusoidal Waves

29 Sinusoidal Waves The distance spanned by one cycle of the motion is called the wavelengthλof the wave. Wavelength is measured in units of meters. During a time interval of exactly one period T, each crest of a sinusoidal wave travels forward a distance of exactly one wavelength λ. Because speed is distance divided by time, the wave speed must be or, in terms of frequency

30 Sinusoidal Waves The angular frequency of a wave is The wave number of a wave is The general equation for the displacement caused by a traveling sinusoidal wave is This wave travels at a speed v = ω/k.

31 Waves in Two and Three Dimensions Suppose you were to take a photograph of ripples spreading on a pond. If you mark the location of the crests on the photo, these would be expanding concentric circles. The lines that locate the crests are called wave fronts, and they are spaced precisely one wavelength apart. Many waves of interest, such as sound waves or light waves, move in three dimensions. For example, loudspeakers and light bulbs emit spherical waves. If you observe a spherical wave very, very far from its source, the wave appears to be a plane wave.

32 Waves in Two and Three Dimensions

33 Waves in Two and Three Dimensions

34 Sound Waves

35 Sound Waves For air at room temperature (20 C), the speed of sound is v sound = 343 m/s. Your ears are able to detect sinusoidal sound waves with frequencies between about 20 Hz and about 20,000 Hz, or 20 khz. Low frequencies are perceived as low pitch bass notes, while high frequencies are heard as high pitch treble notes. Sound waves exist at frequencies well above 20 khz, even though humans can t hear them. These are called ultrasonic frequencies. Oscillators vibrating at frequencies of many MHz generate the ultrasonic waves used in ultrasound medical imaging.

36 EXAMPLE 20.6 Sound wavelengths QUESTION:

37 EXAMPLE 20.6 Sound wavelengths

38 EXAMPLE 20.6 Sound wavelengths

39 EXAMPLE 20.6 Sound wavelengths

40 Electromagnetic Waves A light wave is an electromagnetic wave, an oscillation of the electromagnetic field. Other electromagnetic waves, such as radio waves, microwaves, and ultraviolet light, have the same physical characteristics as light waves even though we cannot sense them with our eyes. All electromagnetic waves travel through vacuum with the same speed, called the speed of light. The value of the speed of light is c = 299,792,458 m/s. At this speed, light could circle the earth 7.5 times in a mere second if there were a way to make it go in circles!

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42 The Index of Refraction Light waves travel with speed c in a vacuum, but they slow down as they pass through transparent materials such as water or glass or even, to a very slight extent, air. The speed of light in a material is characterized by the material s index of refraction n, defined as

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44 Power and Intensity

45 EXAMPLE 20.9 The intensity of a laser beam QUESTION:

46 EXAMPLE 20.9 The intensity of a laser beam

47 EXAMPLE 20.9 The intensity of a laser beam

48 EXAMPLE 20.9 The intensity of a laser beam

49 Intensity and Decibels Human hearing spans an extremely wide range of intensities, from the threshold of hearing at W/m 2 (at midrange frequencies) to the threshold of pain at 10 W/m 2. If we want to make a scale of loudness, it s convenient and logical to place the zero of our scale at the threshold of hearing. To do so, we define the sound intensity level, expressed in decibels (db), as where I 0 = W/m 2.

50 Intensity and Decibels

51 The Doppler Effect An interesting effect occurs when you are in motion relative to a wave source. It is called the Doppler effect. You ve likely noticed that the pitch of an ambulance s siren drops as it goes past you. A higher pitch suddenly becomes a lower pitch. As a wave source approaches you, you will observe a frequency f + which is slightly higher than f 0, the natural frequency of the source. As a wave source recedes away from you, you will observe a frequency f which is slightly lower than f 0, the natural frequency of the source.

52 The Doppler Effect The frequencies heard by a stationary observer when the sound source is moving at speed v 0 are The frequencies heard by an observer moving at speed v 0 relative to a stationary sound source emitting frequency f 0 are

53 EXAMPLE How fast are the police traveling? QUESTION:

54 EXAMPLE How fast are the police traveling?

55 EXAMPLE How fast are the police traveling?

56 EXAMPLE How fast are the police traveling?

57 Chapter 20. Summary Slides

58 General Principles

59 General Principles

60 Important Concepts

61 Important Concepts

62 Applications

63 Applications

64 Applications

65 Chapter 20. Questions

66 Which of the following actions would make a pulse travel faster down a stretched string? A. Use a heavier string of the same length, under the same tension. B. Use a lighter string of the same length, under the same tension. C. Move your hand up and down more quickly as you generate the pulse. D. Move your hand up and down a larger distance as you generate the pulse. E. Use a longer string of the same thickness, density, and tension.

67 Which of the following actions would make a pulse travel faster down a stretched string? A. Use a heavier string of the same length, under the same tension. B. Use a lighter string of the same length, under the same tension. C. Move your hand up and down more quickly as you generate the pulse. D. Move your hand up and down a larger distance as you generate the pulse. E. Use a longer string of the same thickness, density, and tension.

68 The graph at the top is the history graph at x = 4 m of a wave traveling to the right at a speed of 2 m/s. Which is the history graph of this wave at x = 0 m?

69 The graph at the top is the history graph at x = 4 m of a wave traveling to the right at a speed of 2 m/s. Which is the history graph of this wave at x = 0 m?

70 What is the frequency of this traveling wave? A. 0.1 Hz B. 0.2 Hz C. 2 Hz D. 5 Hz E. 10 Hz

71 What is the frequency of this traveling wave? A. 0.1 Hz B. 0.2 Hz C. 2 Hz D. 5 Hz E. 10 Hz

72 What is the phase difference between the crest of a wave and the adjacent trough? A. 0 B. π C. π /4 D. π /2 E. 3 π /2

73 What is the phase difference between the crest of a wave and the adjacent trough? A. 0 B. π C. π /4 D. π /2 E. 3 π /2

74 A light wave travels through three transparent materials of equal thickness. Rank in order, from the largest to smallest, the indices of refraction n 1, n 2, and n 3. A. n 1 > n 2 > n 3 B. n 2 > n 1 > n 3 C. n 3 > n 1 > n 2 D. n 3 > n 2 > n 1 E. n 1 = n 2 = n 3

75 A light wave travels through three transparent materials of equal thickness. Rank in order, from the largest to smallest, the indices of refraction n 1, n 2, and n 3. A. n 1 > n 2 > n 3 B. n 2 > n 1 > n 3 C. n 3 > n 1 > n 2 D. n 3 > n 2 > n 1 E. n 1 = n 2 = n 3

76 Four trumpet players are playing the same note. If three of them suddenly stop, the sound intensity level decreases by A. 4 db B. 6 db C. 12 db D. 40 db

77 Four trumpet players are playing the same note. If three of them suddenly stop, the sound intensity level decreases by A. 4 db B. 6 db C. 12 db D. 40 db

78 Amy and Zack are both listening to the source of sound waves that is moving to the right. Compare the frequencies each hears. A. f Amy > f Zack B. f Amy < f Zack C. f Amy = f Zack

79 Amy and Zack are both listening to the source of sound waves that is moving to the right. Compare the frequencies each hears. A. f Amy > f Zack B. f Amy < f Zack C. f Amy = f Zack