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15 Traveling Waves and Sound

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Types of Waves

A transverse wave

A longitudinal wave

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Waves on Strings and in Air

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Snapshot Graphs

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Constructing a History Graph

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Checking UnderstandingThe 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?

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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?

(b)

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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?

Checking Understanding

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Answer

(d)

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?

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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.

Conceptual Example Problems

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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?

Example Problem

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Sinusoidal Waves

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Checking UnderstandingFor this sinusoidal wave:

1. What is the amplitude?

A. 0.5 m

B. 1 m

C. 2 m

D. 4 m

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Answer For this sinusoidal wave:

1. What is the amplitude?

A. 0.5 m

B. 1 m

C. 2 m

D. 4 m

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Checking UnderstandingFor this sinusoidal wave:

2. What is the wavelength?

A. 0.5 m

B. 1 m

C. 2 m

D. 4 m

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Answer For this sinusoidal wave:

2. What is the wavelength?

A. 0.5 m

B. 1 m

C. 2 m

D. 4 m

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Checking UnderstandingFor this sinusoidal wave:

3. What is the frequency?

A. 50 Hz

B. 100 Hz

C. 200 Hz

D. 400 Hz

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AnswerFor this sinusoidal wave:

3. What is the frequency?

A. 50 Hz

B. 100 Hz

C. 200 Hz

D. 400 Hz

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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?

Example Problems

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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 30-40 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?

Example Problem

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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?

Example Problem

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Sound and Light WavesThe 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.

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