A police car siren emits a sound at 600 Hz.If an observer moves toward the source at 50 km/hr,and the police car approaches the observer at 100 km/hr (all speeds relative to the road),calculate the siren frequency heard by the driver of the police car (assume the speed of sound in air = 343 m/s).
A)626 Hz
B)600 Hz
C)679 Hz
D)577 Hz
E)970 Hz

Question

Quizplus · Accepted Answer

The frequency heard by an observer moving towards the source can be calculated using the formula:

f' = (v + vo) / (v +/- vs) * f

Where:
f = original frequency (600 Hz)
v = speed of sound in air (343 m/s)
vo = velocity of observer towards the source (50 km/hr or 13.89 m/s)
vs = velocity of source towards the observer (-100 km/hr or -27.78 m/s)

Using the above formula, we get:

f' = (343 + 13.89) / (343 - 27.78) * 600
f' = 626.29 ≈ 626 Hz

This is the frequency heard by the observer on the road. However, the question asks for the frequency heard by the driver of the police car. Since the car is stationary relative to itself, the frequency heard by the driver will be the same as that emitted by the siren, i.e. 600 Hz.

Therefore, the best choice is B) 600 Hz.

A Police Car Siren Emits a Sound at 600 Hz