Question

A bat is flying around in a cave, navigating via ultrasonic sound. Assume that the sound emission frequency of the bat is $39000\text{Hz}$. During one fast swoop directly towards a flat wall surface, the bat is moving at $0.025$ times the speed of sound in air. What frequency does the bat hear reflected off the wall?

• A. $4.1\times {10}^4\text{Hz}$
• B. $9.2\times {10}^4\text{Hz}$
• C. $2.2\times {10}^4\text{Hz}$
• D. $9.2\times {10}^2\text{Hz}$

Answer 1

The correct option is A $4.1\times {10}^4\text{Hz}$

Given that,
frequency of sound emitted by bat $=39000\text{Hz}$
Let speed of sound in air be $v$
speed of bat $=0.025v$

By using Doppler effect formula, frequency received by bat
$f_r=f\left(\frac{v+v_{\text{bat}}}{v-v_{\text{bat}}}\right)$
$\Rightarrow f_r=3.9\times {10}^4\left(\frac{v+v\times 0.025}{v-v\times 0.025}\right)$
$\Rightarrow f=4.1\times {10}^4\text{Hz}$