Question

A bat emitting an ultrasonic wave. of frequency $4.5\times {10}^4$ Hz flies at a speed of 6 m/s between two parallel walls. Find the two frequencies heard by the bat and the beat frequency between the two. The speed sound is 330 m/s.

Answer 1

Let the bat be flying between three walls $W_1{W}_2.$

So it will listen two frequency reflecting from walls $W_2$ and $W_1.$

So, apparent frequency, as received by wall W,

$f{W}_2=\left(\frac{330+0+0}{330-0.6}\right)\times f=\frac{330}{324}$

Therefore app. frequency received by the bat from wall $W_2$ is given by

$F_{B2}$ of wall $W_1$

$=\left(\frac{330+0-(-6)}{330+0+0}\right)f_1{W}_2$

$=\left(\frac{336}{330}\right)\times \left(\frac{330}{324}\right)f$

Similarly, the apparent frequency received by the bat from wall $W_1$ is,

$f_{B1}=\left(\frac{324}{336}\right)f$

So the beat frequency heard by the bat

$=4.67\times {10}^4-4.3430\times {10}^4$

=3270 Hz.