question_answer

The driver of a car travelling with speed \[30\,m{{s}^{-2}}\] towards a hill sounds a horn of frequency 600 Hz. If the velocity of sound in air is \[330\,m{{s}^{-1}},\] tile-frequency of reflected sound as heard by driver is [AIPMT (S) 2009]

A)  550 Hz            

B)       555.5 Hz         

C)  720 Hz            

D)       500 Hz

Correct Answer: C

Solution :

Key Idea Apply Doppler's effect.

Whenever there is a relative motion between a source of sound and the observer (listener), the frequency of sound heard by the observer is different from the actual frequency of sound emitted by source.

Case I

Case II

[for case I]  \[n'=\frac{v}{v-30}n\]                       ...(i)

[for case II]\[n''=\frac{v+30}{v}n'\]                      ... (ii)

From Eqs. (i) and (ii), we get

\[n''=\frac{v+30}{v-30}n=\frac{360}{300}\times 600=720\,Hz\]

\[=720\,Hz\]