Question

Two sources of sound $S_1\text{and}{S}_2$, produce sound waves of same frequency of $660\text{Hz}$. A listener is moving from source $S_1\text{towards}{S}_2$, with a constant speed $u\text{m/s}$ and he hears $10\text{beats/s}$. The velocity of sound is $330\text{m/s}$. Then $u$ equals

• A. $2.5\text{m/s}$
• B. $15.0\text{m/s}$
• C. $10.0\text{m/s}$
• D. $5.5\text{m/s}$

Answer 1

The correct option is A $2.5\text{m/s}$

Let the apparent frequencies heard by the observer are $f_1$ , for source $S_1$ and $f_2$ for source $S_2$.

$f_1=f\left(\frac{v-u}{v}\right)\text{and}{f}_2=f\left(\frac{v+u}{v}\right)$

As $f_2>f_1$, the beat frequency is, $f^{\prime }=f_2-f_1$

$\Rightarrow f^{\prime }=f\left(\frac{v+u}{v}\right)-f\left(\frac{v-u}{v}\right)$

$f_2-f_1=f\times \frac{2u}{v}$

$\Rightarrow 10=660\times \frac{2u}{330}$

$\therefore u=2.5\text{m/s}$

Hence, $\left(C\right)$ is the correct answer.