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A horn produces sound with frequency f0. Let the frequency
Chapter 14, Problem 42P(choose chapter or problem)
Problem 42P
A horn produces sound with frequency f0. Let the frequency you hear when you are at rest and the horn moves toward you with a speed u be f1, let the frequency you hear when the horn is at rest and you move toward it with a speed u be f2.(a) Is f1 greater than, less than, or equal to f2? (b) Choose the best explanation from among the following:
I. A moving observer encounters wave crests more often than a stationary observer, leading to a higher frequency.
II. The relative speeds are the same in either case. Therefore, the frequencies will be the same as well.
III. A moving source causes the wave crests to “bunch up,” leading to a higher frequency than for a moving observer.
Questions & Answers
QUESTION:
Problem 42P
A horn produces sound with frequency f0. Let the frequency you hear when you are at rest and the horn moves toward you with a speed u be f1, let the frequency you hear when the horn is at rest and you move toward it with a speed u be f2.(a) Is f1 greater than, less than, or equal to f2? (b) Choose the best explanation from among the following:
I. A moving observer encounters wave crests more often than a stationary observer, leading to a higher frequency.
II. The relative speeds are the same in either case. Therefore, the frequencies will be the same as well.
III. A moving source causes the wave crests to “bunch up,” leading to a higher frequency than for a moving observer.
ANSWER:
Step 1 of 2
Part a
We are required to compare the frequency when the source is moving with the frequency
when the observer is moving.
From Doppler’s law,
The frequency , when the source is moving.
The frequency , when the observer is moving.
If we consider the two equations, we will find that
.
Therefore, the frequency of the horn will be greater than the frequency of the observer.