Question

A bat is fitting 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

Given :

Ultrasonic beep frequency of the bat, υ = 40 kHz

Velocity of the bat, v$\sf _{b}$ = 0.03 v

To find :

The frequency of the bat hear.

Solution :

The apparent frequency of the sound striking the wall is given by,

$\dashrightarrow\sf v' = \bigg( \dfrac{v}{v- v_b}\bigg) \upsilon$

by substituting the values in the formula,

$\dashrightarrow\sf v' = \bigg( \dfrac{v}{ v- 0.33}\bigg) \times 40$

$\dashrightarrow\sf v' = \dfrac{40}{0.97} kHz$

The frequency is reflected by the stationary wall towards the bat.

The frequency of the received sound is given by,

$\dashrightarrow\sf v'' = \bigg( \dfrac{v + v_b}{v}\bigg) v'$

$\dashrightarrow\sf v'' = \bigg( \dfrac{v + 0.03v}{v}\bigg) \dfrac{40}{0.97}$

$\dashrightarrow\sf v'' = \dfrac{ 1.03 \times 40}{0.97}$

$\dashrightarrow \boxed{\sf v'' = 42.47 \: kHz}$