Question

A bat moving at $10m{s}^{-1}$ towards a wall sends a sound signal of 8000 Hz 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. 8000
• C. 8516
• D. 8424

Answer 1

The correct option is C 8516

the time taken relative to bat for sound wave to travel distance S between consecutive wave front traveling towards wall is
$T=\frac{S}{V_{sound/bat}}=\frac{1}{8000}$
$V_{sound/bat}=V_{sound}-V_{bat}$
$T=\frac{S}{V_{sound}-V_{bat}}=\frac{1}{8000}$...(i)
After reflection as the bat is moving towards wall the time taken by sound to travel distance S is given as
$T^{\prime }=\frac{S}{V_{sound}+V_{bat}}$...(ii)
substituting value of S from equation (i) in (ii)
$T^{\prime }=\frac{\frac{V_{sound}-V_{bat}}{8000}}{V_{sound}+V_{bat}}$...(iii)
The apparent frequency will be $f^{\prime }=\frac{1}{T^{\prime }}$
$f^{\prime }=\frac{V_{sound}+V_{bat}}{V_{sound}-V_{bat}}8000$
$f^{\prime }=\frac{10+320}{320-10}8000$
$f^{\prime }=8516$ Hz
Hence correct answer is D.