1. Traveling Waves and Sound
Chapter 15
Traveling Waves and Sound

2. 15 Traveling Waves and Sound
Slide 15-2

3. Slide 15-3

4. Slide 15-4

5. Slide 15-5

6. Types of Waves
A transverse wave
A longitudinal wave
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7. Waves on Strings and in Air
Slide 15-13

8. Snapshot Graphs
Slide 15-14

9. Constructing a History Graph
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10. Checking Understanding
The graph below shows a snapshot graph of a wave on a string that is moving to the right. A point on the string is noted. Which of the choices is the history graph for the subsequent motion of this point?
Answer: B
Slide 15-16

11. Answer
The graph below shows a snapshot graph of a wave on a string that is moving to the right. A point on the string is noted. Which of the choices is the history graph for the subsequent motion of this point?
Answer: B
(b)
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12. Checking Understanding
The graph below shows a history graph of the motion of one point on a string as a wave moves by to the right. Which of the choices is the correct snapshot graph for the motion of the string?
Answer: D
Slide 15-18

13. Answer
The graph below shows a history graph of the motion of one point on a string as a wave moves by to the right. Which of the choices is the correct snapshot graph for the motion of the string?
Answer: D
(d)
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14. Conceptual Example Problems
A wave travels back and forth on a guitar string; this is responsible for making the sound of the guitar, as we will see. As the temperature rises, the tension in a guitar string decreases. How does this change the speed of a wave on the string?
How do you measure the temperature of a flame if the temperature is higher than a probe can handle? One possible solution is to use sound. A source emits a pulse of sound on one side of the flame, which is then measured by a microphone on the other side. A measurement of the time between the emission and the reception of the pulse allows a determination of the temperature. Explain how this technique works.
Slide 15-20

15. Example Problem
A particular species of spider spins a web with silk threads of density 1300 kg/m3 and diameter 3.0 µm. A typical tension in the radial threads of such a web is 7.0 mN. If a fly lands in this web, which will reach the spider first, the sound or the wave on the web silk?
Slide 15-21

16. Sinusoidal Waves
Slide 15-22

17. Checking Understanding
For this sinusoidal wave:
What is the amplitude?
0.5 m
1 m
2 m
4 m
Answer: B
Slide 15-23

18. Answer For this sinusoidal wave: What is the amplitude? 0.5 m 1 m 2 m
Answer: B
Slide 15-24

19. Checking Understanding
For this sinusoidal wave:
What is the wavelength?
0.5 m
1 m
2 m
4 m
Answer: C
Slide 15-25

20. Answer For this sinusoidal wave: What is the wavelength? 0.5 m 1 m 2 m
Answer: C
Slide 15-26

21. Checking Understanding
For this sinusoidal wave:
What is the frequency?
50 Hz
100 Hz
200 Hz
400 Hz
Answer: B
Slide 15-27

22. Answer For this sinusoidal wave: What is the frequency? 50 Hz 100 Hz
Answer: B
Slide 15-28

23. Example Problems
The new generation of cordless phones use radio waves at a frequency of 5.8 GHz. What is the wavelength of these radio waves?
A speaker emits a tone of a particular frequency. Suppose the air temperature increases. What happens to the wavelength of the sound?
Slide 15-29

24. Example Problem
The water in the open ocean is in constant motion, carrying long-wavelength waves moving at relatively high speeds. Under steady winds, the amplitude of these waves can get quite large. Suppose a boat is at rest in the open ocean. The wind has created a steady wave with wavelength 190 m traveling at 14 m/s. (In fact, the ocean will support a mix of waves, but for steady winds of knots, this is the most prevalent wavelength, and the correct speed for a wave of this wavelength in deep water.) The top of the crests of the waves is 2.0 m above the bottom of the troughs. (This wave height is quite typical for windy days in the Atlantic Ocean. The Southern Ocean, with its planet-circling stretch of open water, supports much larger waves—wave heights of 7 m are quite common.) What is the maximum vertical speed of the boat as it bobs up and down on the passing wave? What is the maximum vertical acceleration?
Slide 15-30

25. Example Problem
Let’s use the data from the previous problem again. Suppose the boat is sailing at 6.0 m/s in the same direction as the motion of the waves. At t  0 s the boat is at the bottom of a trough. How high above this lowest point will the boat be at t  10 s?
Slide 15-31

26. Sound and Light Waves The speed of sound varies with the medium.
Light and other electromagnetic waves in vacuum and in air move at the same speed, 3.00 x 108 m/s.
Slide 15-32

27. The Doppler Effect
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28. Example Problem
A Doppler ultrasound unit is used to measure the motion of blood in a patient’s artery. The probe has a frequency of 5.0 MHz, and the maximum frequency shift on reflection is 400 Hz. What is the maximum speed of the blood in the artery?
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29. Energy and Intensity
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30. The Decibel Scale Sound intensity level is measured in decibels.
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31. Example Problems
If you are standing 2.0 m from a lamp that is emitting 100 W of infrared and visible light, what is the intensity of radiation on your skin? How does this compare with the intensity of sunlight, approximately 1000 W/m2 at the surface of the earth?
Suppose it was so quiet outside that you could detect a sound at the threshold of your perception, 0 dB. Now suppose that someone was playing a stereo with the volume cranked up all the way. How far away could you detect the sound from the stereo?
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32. Example Problem
You are working in a shop where the noise level is a constant 90dB.
Your eardrum has a diameter of approximately 8.4 mm. How much power is being received by one of your eardrums?
This level of noise is damaging over a long time, so you use earplugs that are rated to reduce the sound intensity level by
26 dB, a typical rating. What is the power received by one eardrum now?
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33. Example Problem
Your ears are, in principle, sensitive to sound down to 0 dB. In practice, though, background noise limits your threshold of hearing to about 20 dB. Suppose that someone is playing a stereo with the volume cranked up all the way, giving a sound intensity level of
110 dB at a distance of 1.0 m. How far away could you be and still hear the music? That is, at what distance from the stereo would the sound intensity level be 20 dB? (This example is a bit artificial because loss mechanisms work at these great distances and any practical situation would involve reflections, but it is instructive.)
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34. Summary
Slide 15-40

35. Summary
Slide 15-41

36. Additional Questions
A snapshot and a history graph for a sinusoidal wave on a string appear as follows:
What is the speed of the wave?
1.5 m/s
3.0 m/s
5.0 m/s
15 m/s
Answer: B
Slide 15-42

37. Answer
A snapshot and a history graph for a sinusoidal wave on a string appear as follows:
What is the speed of the wave?
1.5 m/s
3.0 m/s
5.0 m/s
15 m/s
Answer: B
Slide 15-43

38. Additional Example Problems
A 5.0 kg block is hung from the ceiling on a 2.0-meter-long metal wire with a mass of 4 g. The wire is “plucked” at the very bottom, where it connects to the block. How long does it take the pulse to reach the ceiling?
The intensity of sunlight is approximately 1000 W/m2 at the surface of the earth. Saturn is about 10 times as far from the sun as the earth. If the earth were moved to the distance of Saturn, what would be the intensity of sunlight at the surface?
Suppose you are powering a spacecraft with a 1.0 m2 array of solar cells with an efficiency of 12%. Above the earth’s atmosphere, where the intensity of sunlight is approximately 1300 W/m2, what is the maximum power you could get from the solar cells? How much power could you get if your spacecraft was nearing Neptune, 30 times as far from the sun as the earth?
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