First slide

Doppler

Question

A car is moving towards a high cliff. The driver sounds a horn of frequency f. The reflected sound heard by the driver has a frequency 2 f. If v be the velocity of sound, then the velocity of the car, in the same velocity units would be

Moderate

A

$\frac{v}{4}$
B

$\frac{v}{2}$
C

$\frac{v}{\sqrt{2}}$
D

$\frac{v}{3}$

Solution

$w h e n d r i v e r i s a p p r o a c h i g t h e w a l l t h e o b s e r v e r a n d v i r t u a l s o u r c e a p p r o a c h e a c h o t h e r w i t h s a m e v e l o c i t y a p p a r e n t f r e q u e n c y f^{1} = \frac{v + v_{0}}{v - v_{0}} f = 2 f s o l v i n g f o r v_{0} w e g e t v_{0} = \frac{v}{3}$

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