Question
Asked Apr 28, 2019
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If people on the stationary ship hear a beat frequency of 4.0 Hz , what is the speed of the approaching ship? If people on the stationary ship hear a beat frequency of 4.0 Hz , what is the speed of the receding ship?

Two ships in a heavy fog are blowing their horns, both of which
produce sound with a frequency of 200.0 Hz (see the
figure(Figure 1)). One ship is at rest, the other moves on a
straight line that passes through the one at rest.0
igure
1 of 1
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Two ships in a heavy fog are blowing their horns, both of which produce sound with a frequency of 200.0 Hz (see the figure(Figure 1)). One ship is at rest, the other moves on a straight line that passes through the one at rest.0 igure 1 of 1

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Expert Answer

Step 1

Speed of sound in air is 343 m/s. The given information is:

 

One ship is at rest and the other moves along the straight line that passes through the one at rest.

The frequencies of the sound produced by the horns on both the ships are 200 Hz respectively. The beat frequency of the sound heard by the people on the stationary ship is 4.0 Hz.

Step 2

(a)

 

The moving ship is approaching the stationary ship. The expression for the Doppler effect when the source is approaching towards the stationary observer is:

 

Here, f’ is the observed frequency, v is the speed of the sound, u is the speed of the source and f is the frequency emitted by the source.

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Step 3

Since the moving ship approaches the stationa...

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