First slide

Doppler

Question

A siren emitting a sound of frequency $800 Hz$ moves away from an observer towards a cliff at a speed of $15 m s^{- 1}$ . Then, the frequency of sound that the observer hears in the echo reflected from the cliff is? (The Velocity of Sound in air $= 330 m s^{- 1})$

Moderate

A

$838 Hz$
B

$885 Hz$
C

$765 Hz$
D

$800 Hz$

Solution

$Here, frequency of sound emitted by siren, v_{0} = 800 Hz$
$Speed of source, v_{s} = 15 m s^{- 1}$
$Speed of sound in air, v = 330 m s^{- 1}$
$A p p a r e n t f r e q u e n c y o f s o u n d a t t h e c l i f f = f r e q u e n c y h e a r d b y o b s e r v e r = v$
$Using Doppler's effect of sound$
$v = (\frac{v}{v - v_{s}}) v_{0} = \frac{330}{330 - 15} \times 800$
$= \frac{330}{315} \times 800 = 838.09 Hz \approx 838 Hz$

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