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© 2010 Pearson Education, Inc. Slide 15-2

15 Traveling Waves and Sound

© 2010 Pearson Education, Inc.

Reading Quiz

1. Which of the following is a longitudinal wave?

A. sound wave

B. water wave

C. light wave

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1. Which of the following is a longitudinal wave?

A. sound wave

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Answer


Reading Quiz

2. When the particles of a medium move with simple harmonic motion, this means the wave is

A. a sound wave

B. a sinusoidal wave

C. a standing wave

D. a harmonic wave

E. a transverse wave

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2. When the particles of a medium move with simple harmonic motion, this means the wave is

B. a sinusoidal wave

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Answer


Reading Quiz

3. We measure the sound intensity level in units of

A. watts

B. joules

C. candelas

D. decibels

E. hertz

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3. We measure the sound intensity level in units of

D. decibels

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Answer


In air => 340 m/s

In Helium => 970 m/s

In water => 1480 m/s

In Human tissue (ultrasound) => 1540 m/s

In Aluminum => 5100 m/s

In Granite => 6000 m/s

In Diamond => 12,000 m/s

Speed of Sound

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Sinusoidal Waves

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Sound and Light WavesThe speed of sound and other mechanical waves 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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Clicker Questions

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A snapshot and a history graph for a sinusoidal wave on a string appear as follows:

What is the speed of the wave?A. 1.5 m/sB. 3.0 m/sC. 5.0 m/sD. 15 m/s

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A snapshot and a history graph for a sinusoidal wave on a string appear as follows:

What is the speed of the wave?

B. 3.0 m/s

Answer


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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The Doppler Effect

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The Doppler Effect

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Example ProblemA 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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Energy and Intensity

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The Decibel ScaleSound intensity level is measured in decibels.

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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?

Example Problems

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You are working in a shop where the noise level is a constant 90dB.

A. Your eardrum has a diameter of approximately 8.4 mm. How much power is being received by one of your eardrums?

B. This level of noise is damaging over a long time, so you use earplugs that are rated to reduce the sound intensity level by26 dB, a typical rating. What is the power received by one eardrum now?

Example Problem

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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 of110 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.)

Example Problem

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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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Additional Examples

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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