Chapter 6: Problem 23

A recording of a high-frequency pure tone is played through both speakers of a portable stereo placed in an open field. A person a few meters in front of the stereo walks slowly along an arc around it. How does the sound that is heard change as the person moves?

Short Answer

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Answer: As the person moves along the arc, the perceived sound changes due to differences in distances from each speaker and interference patterns caused by these differences. The person will experience varying loudness (amplitude) of the high-frequency pure tone due to the short wavelength, which causes constructive or destructive interference as a result of different sound wave arrival times at the person's ears.

Step by step solution

Identify the sound source and the observer.

In this exercise, the sound source is the portable stereo with two speakers playing a high-frequency pure tone. The observer is the person walking along an arc a few meters in front of the stereo.

Observe the change in distance between the speakers and the person.

As the person moves along the arc, the distance between them and each speaker will change. When the person is directly in front, the distances from both speakers are equal. As they move along the arc, the distance from one speaker will increase while the distance from the other will decrease.

Consider the interference patterns.

The differences in distance from each speaker result in different sound wave arrival times at the person's ears. These differences can cause constructive or destructive interference of the sound waves, leading to changes in the loudness (amplitude) of the perceived sound.

Account for the high-frequency pure tone.

Since the sound has a high frequency, its wavelength is relatively short. Due to this short wavelength, the distances needed for constructive or destructive interference to occur are smaller compared to low-frequency sounds. As a result, the listener is more likely to perceive variations in the sound amplitude as they move along the arc.

Describe the perceived sound changes as the person moves along the arc.

As the person moves along the arc, the sound heard will change due to the differences in distances from each speaker and interference patterns caused by these differences. As a result, the person will experience varying loudness (amplitude) of the high-frequency pure tone played by the portable stereo.

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A recording of a high-frequency pure tone is played through both speakers of a portable stereo placed in an open field. A person a few meters in front of the stereo walks slowly along an arc around it. How does the sound that is heard change as the person moves?

Short Answer

Step by step solution

Identify the sound source and the observer.

Observe the change in distance between the speakers and the person.

Consider the interference patterns.

Account for the high-frequency pure tone.

Describe the perceived sound changes as the person moves along the arc.

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