Question

If the bat emits a sound at a frequency of 80.2 kHzkHz and hears it reflected at a frequency of 83.5 kHzkHz while traveling at a speed of 3.9 m/sm/s , calculate the speed of the insect.

Answer 1

To solve this problem we will apply the concepts related to the Doppler Effect. The Doppler effect is the change in the perceived frequency of any wave movement when the emitter, or focus of waves, and the receiver, or observer, move relative to each other.

Mathematically it can be described as

$v' = v (\frac{f' ( v - v_{bat}) - f ( v + v_{bat})}{f'(v-v_{bat}) + f ( v + v_{bat})})$

Where,

v = Speed of sound

f' = Reflected frequency

f = Emitted Frequency

$v_{bat}$ = Speed of the object

Assuming that the speed of the medium is the speed of sound of 343m / s, we will then have that:

$v' = 343 (\frac{(83.5) (343 -3.9) - 80.2(343+3.9)}{83.5(343-3.9) + 80.2(343+4.3)})$

$v' = 3.0134m/s$