Question

A bat emits a sound at a frequency of 30.0 kHz as it approaches a wall. The bat detects beats such that the

frequency of the echo is 900 Hz higher than the frequency the bat is emitting. What is the speed of the bat? The
speed of sound in air is 340 m/s.

Answer 1

5.02 m/s

Step-by-step explanation:

given,

frequency of sound emitted by bat,
`f_1` = 30 kHz = 30000 Hz

beat frequency detected by bat
`f_b` = 900 Hz

Speed of sound, v = 340 m/s

`f_b = f_1 -f_2`

`900 = 30000-f_2`

`f_2 = 30900`

Using Doppler's effect formula

`f_2=f_1((v+v_b)/(v-v_b))`

`v_b = velocity\ of\ bat`

`30900=30000((340+v_b)/(340-v_b))`

`1.03 =((340+v_b)/(340-v_b))`

`v_b = 5.02 m/s`

Hence, the speed of bat is equal to 5.02 m/s