S1 & S2 are sources of the sound of frequency 656 Hz. S1 is moving along OP and S2 is moving on the circle in an anticlockwise direction with a constant speed of 4√2 m\s. P is a detector that is fixed. Select the correct options (Vsound=300m\s)
- When S2 is at Q, Then frequency it detected by the detector is approximately 647 Hz.
- When S2 is at Q, Then frequency it detected by the detector is 327 Hz.
- When S2 is at R and S1 is coming toward P with a velocity of 4m/s, Then the beat frequency it detected by the detector is 8.86 Hz.
- When S2 is at R and S1 is coming toward P with a velocity of 4m/s, Then the beat frequency it detected by the detector is 2.56 Hz.
The Correct Option is A, C
Solution and Explanation
\(f'=\frac{656\times300}{304}\)
\(f'=647.36\,Hz\)
Hence, Option (A) is correct.
From S2 , \(f'=656\,[\frac{300}{300+4\sqrt2\,cos\,90}]\)
\(f'=656\)
From S1, \(f''=656\,[\frac{300}{300-4}]\)
\(f''=664.86\)
Beat frequency = \(f''-f'\) = \(664.86-656\) = 8.86 Hz
br>Hence, Option (C) is also correct.
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Concepts Used:
Doppler Effect
The Doppler effect is a phenomenon caused by a moving wave source that causes an apparent upward shift in frequency for observers who are approaching the source and a visible downward change in frequency for observers who are retreating from the source. It's crucial to note that the impact isn't caused by a change in the source's frequency.
The Doppler effect may be seen in any wave type, including water waves, sound waves, and light waves. We are most familiar with the Doppler effect because of our encounters with sound waves