question_answer

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

A)  550 Hz                        

B)  555.5 Hz

C)  720 HZ                        

D)  500 Hz

Correct Answer: C

Solution :

 When the sound is reflected from the cliff, it approaches the driver of the car. Therefore, the driver acts as an observer and both the source (car) and observer are moving. Hence, apparent frequency heard by the observer (driver) is given by \[f'=f\left( \frac{v+{{v}_{0}}}{v-{{v}_{0}}} \right)\]                                           (i) where\[v=\]velocity of sound, \[{{v}_{0}}=\]velocity of car \[={{v}_{s}}\] Frequency of reflected sound heard by driver \[f'=f\left( \frac{v+{{v}_{O}}}{v-{{v}_{S}}} \right)=600\left( \frac{330+30}{330-30} \right)=720\,Hz\]