A 550-Hz whistle is moved toward a listener at a speed of 25.0 m/s.At the same time,the listener moves at a speed of 35.0 m/s in a direction away from the whistle.What is the apparent frequency heard by the listener? (The speed of sound is 340 m/s. )
A)510 Hz
B)533 Hz
C)655 Hz
D)460 Hz
E)594 Hz

Question

Quizplus · Accepted Answer

To find the apparent frequency heard by the listener, we need to use the formula for Doppler effect:

f' = f (v + v₀)/(v - vₛ)

where 
f = frequency emitted by the whistle (550 Hz) 
v = speed of sound (340 m/s) 
v₀ = speed of the listener (35.0 m/s) 
vₛ = speed of the source (whistle) (25.0 m/s, but negative since it's moving towards the listener)

Plugging in the values, we get:

f' = 550 * (340 + 35)/(340 - (-25)) 
f' = 550 * 375/365 
f' ≈ 533 Hz

Therefore, the best choice is B, with an explanation as shown above.

A 550-Hz Whistle Is Moved Toward a Listener at a Speed