Question

A bat emitting an ultrasonic wave of frequency 4.5 × 104 Hz flies at a speed of 6 m s−1 between two parallel walls. Find the fractional heard by the bat and the beat frequencies heard by the bat and the beat frequency between the two. The speed of sound is 330 m s−1.

Answer 1

Speed of bat v = 6 ms−1

Frequency of ultrasonic wave f = 4.5 × 104 Hz

Velocity of bird vs = 6 ms−1

Let us assume that the bat is flying between the walls X and Y.

Apparent frequency received by the wall Y is

f'=(vv−vs)×f0⇒f'=(330330−6)×4.5×104⇒f'=4.58×104 Hz

Now, the apparent frequency received by the bat after reflection from the wall Y is given by:

f"=(v+vsv)×fx⇒f"=(330+6330)×4.58×104⇒f"=4.66×104 Hz

Frequency of ultrasonic wave received by wall X:

n'=330330+6×4.5×104   =4.41×104 Hz

The frequency of the ultrasonic wave received by the bat after reflection from the wall X is

n"=v−vsv×n'   =330−6330×4.41×104   =4.33×104 Hz

 Beat frequency heard by the bat is

=4.66×104