Question

A bat is flitting about in a cave navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in air. What frequency does the bat hear reflected off the wall ?

Answer 1

Ultrasonic beep frequency emitted by the bat, $f=40kHz$
Velocity of the bat, $v_b=0.03v$
where, $v=$ velocity of sound in air
The apparent frequency of the sound striking the wall is given as:

$f^{\prime }=\left(\frac{v}{v-v_b}\right)f$

$=\left(\frac{v}{v-0.03v}\right)\times 40$

$=\frac{40}{0.97}kHz$

This frequency is reflected by the stationary wall $\left(f_s\right)$ toward the bat.

The frequency $\left(f^{\prime \prime }\right)$ of the received sound is given by the relation:

$f^{\prime \prime }=\left(\frac{v+v_b}{v}\right)f^{\prime }$

$=\left(\frac{v+0.03v}{v}\right)\times \frac{40}{0.97}$

$=\frac{1.03\times 40}{0.97}=42.47kHz$