A bat is flying toward a cave wall. If it hears reflected sound of frequency 60.9 kHz, what is its flying speed, assuming it emits sound at 52.0 kHz? The speed of sound is 341.5 m/s.
A) 25.9 m/s
B) 28.1 m/s
C) 49.9 m/s
D) 26.9 m/s
E) 58.4 m/s

Question

Quizplus · Accepted Answer

We can use the formula:
f' = f (v + vs) / (v - vb)
Where
f = emitted frequency
f' = reflected frequency
v = speed of sound
vs = speed of the source (the bat)
vb = speed of the observer (the cave wall)
We are given:
f = 52.0 kHz, f' = 60.9 kHz, v = 341.5 m/s
vb = 0 (since the cave wall is stationary)
Solving for vs, we get:
vs = f' * (v - vb) / f - v
vs = 60.9 kHz * 341.5 m/s / (52.0 kHz + 341.5 m/s)
vs ≈ 26.9 m/s

Therefore, the flying speed of the bat is approximately 26.9 m/s.
The answer is D.

A Bat Is Flying Toward a Cave Wall