First slide

Doppler's effect

Question

A racing car moving towards a cliff, sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If v is the velocity of sound, then the velocity of the car is

Moderate

A

$v / \sqrt{2}$
B

$v / 2$
C

$v / 3$
D

$v / 4$

Solution

Frequency of reflected sound heard by driver $n^{'} = n (\frac{v + v_{0}}{v - v_{S}})$
It is given that $n^{'} = 2 n$
Hence, $2 n = n (\frac{v + v_{car}}{v - v_{car}}) \Rightarrow v_{car} = v / 3 .$

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