A bat emits a sound at a frequency of 39.0 kHz as it approaches a wall. The bat detects beats with a frequency of 827 Hz between the sound it emits and the echo bouncing from the wall. What is the speed of the bat? The speed of sound in air is 343 m/s.
A) 2.7 m/s
B) 3.0 m/s
C) 3.6 m/s
D) 5.4 m/s
E) 9.0 m/s

Question

Quizplus · Accepted Answer

Firstly, let's find the wavelength of the sound wave emitted by the bat using the formula:

wavelength = speed of sound / frequency = 343 m/s / 39.0 kHz = 0.00879 m

Now, let's find the relative speed of the bat and the wall using the formula:

beat frequency = (speed of sound / (speed of sound - relative speed))*emitted frequency - reflected frequency

827 Hz = (343 m/s / (343 m/s - relative speed))*39.0 kHz - 39.0 kHz

Simplifying this equation, we get:

relative speed = 3.60 m/s

Therefore, the best choice is C, 3.6 m/s.

A Bat Emits a Sound at a Frequency of 39