Question

Two sources $S_{1}$ and $S_{2}$ of same frequency $f$ emits sound. The sources are moving as shown with speed $u$ each. A stationary observer hears that sound. The beat frequency is :- $\left(\right.v=$ velocity of sound $\left.$

• A. $\frac{2 u^{2} f}{v^{2} - u^{2}}$
• B. $\frac{2 v^{2} f}{v^{2} - u^{2}}$
• C. $\frac{2 u v f}{v^{2} - u^{2}}$
• D. $\frac{2 u}{v}f$

Answer 1

Answer: (C)

$f_{1}=f\left(\frac{v}{v - u}\right),f_{2}=f\left(\frac{v}{v + u}\right)$
Beats $=f_{1}-f_{2}=fv\left(\frac{1}{v - u} - \frac{1}{v + u}\right)$
$=\frac{2 u v f}{v^{2} - u^{2}}$