Question

A bat moving at $10m{s}^{-1}$ towards a wall sends a sound signal of $8000Hz$ towards it. On reflection it hears a sound of frequency $f$. The value of $f$ in $Hz$ is close to (speed of sound = $320m{s}^{-1}$)

• A. 8258
• B. 8516
• C. 8000
• D. 8424

Answer 1

Answer: (B)

Observer $O$ at the wall receives a frequency, $f_1=f\frac{v}{v-v_p}$
Here $v=$ speed of sound $=320m/s$
On reflection from the wall, source $S$ received
$f_2=f_1\frac{v+v_s}{v}$
$\Rightarrow f_2=f\frac{v+v_s}{v-v_s}=8000\left(\frac{320+10}{320-10}\right)=8000\times \frac{339}{3199}$
$\Rightarrow f_2=8516.12\approx 8516Hz$