Question

Two persons A and B, each carrying a source of sound of frequency $f$, are standing a few metres apart in a quiet field. A starts moving towards B with a speed $u$. If $v$ is the speed of sound, the number of beats heard per second by A will be

• A. $\frac{fu}{v}$
• B. $\frac{2fu}{v}$
• C. $\frac{fu}{(v+u)}$
• D. $\frac{fu}{(v-u)}$

Answer 1

The correct option is A $\frac{fu}{v}$

Person A hears the sound of his own source whose frequency in $f$. He also hears the sound of the source carried by person B, towards whom he is moving with a speed $u$.
The apparent frequency of this sound, $f^{\prime }=f(1+\frac{u}{v})$
$\Rightarrow f^{\prime }-f=\frac{fu}{v}$
$\therefore$ Beat frequency $f_b=f^{\prime }-f=\frac{fu}{v}$
Hence, the correct choice is (a).