First slide

Doppler

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 be the velocity of sound, the velocity of the car u is

Moderate

A

$V / \sqrt{2}$
B

$V / 2$
C

$V / 3$
D

$V / 4$

Solution

Frequency received by driver after reflection from wall is given by
$n^{'} \equiv n (\frac{v + u}{v - u}) where = velocity of car moving towards wall If the car is moving away from wall, then n^{''} = n (\frac{v - u}{v + u}) Given that n = 2 n Here, octave means double to original hequency n (\frac{v + u}{v - u}) = 2 n or v + u = 2 v - 2 u or u = v / 3$

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