question_answer

Two sirens situated one kilometer apart are producing sound of frequency 330 Hz. An observer starts moving from one siren to the other with a speed of 2 m/s. If the speed of sound be 330 m/s, what will be the beat frequency heard by the observer                                         [RPMT 1996; CPMT 2002]

A)            8    

B)            4

C)            6    

D)            1

Correct Answer: B

Solution :

           Observer is moving away from siren 1 and towards the siren 2. Hearing frequency of sound emitted by siren 1                    \[{{n}_{1}}=n\left( \frac{v-{{v}_{0}}}{v} \right)=330\,\left( \frac{330-2}{330} \right)=328Hz\]                    Hearing frequency of sound emitted by siren 2                    \[{{n}_{2}}=n\,\left( \frac{v+{{v}_{0}}}{v} \right)=330\,\left( \frac{330+2}{330} \right)=332Hz\] Hence, beat frequency \[={{n}_{2}}-{{n}_{1}}=332-328=4.\]