Question

A bat moving at $10ms^{- 1}$ towards a wall sends a sound signal of $8000\text{Hz}$ towards it. On reflection, it hears a sound of frequency $f$ . The value of $f$ in $\text{Hz}$ is close to

$\left(\right.\text{speed of sound}=320 \, ms^{- 1}\left.\right)$

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

Answer 1

Answer: (D)

We can assume that reflected wave is due to image of $\text{B}$ coming with same speed in opposite direction

Observer
$f= \, \frac{v + 10}{v - 10} \, \times f_{0}$
$ \, = \, \frac{320 + 10}{320 - 10} \, \times 8000$
$ \, = \, \frac{330}{310} \, \times 8000$
$ \, = \, \frac{33}{31} \, \times 8000$
$= \, 8516 \, Hz$