Question

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)

• A. When S2 is at Q, Then frequency it detected by the detector is approximately 647 Hz.
• B. When S2 is at Q, Then frequency it detected by the detector is 327 Hz.
• C. 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.
• D. 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.

Answer 1

Answer: (A), (C)

When S2 is at Q, Then frequency it detected by the detector is approximately 647 Hz.

Answer 2

The correct options are (A) and (C).

$f'=\frac{656\times300}{304}$

$f'=647.36\,Hz$

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.