An ambulance is traveling East at 20m/s. The siren emits a fixed frequency of 45

Question

An ambulance is traveling East at 20m/s. The siren emits a fixed frequency of 450Hz. Each of the following cars is traveling down the road as described. Determine if the driver of the car will hear a frequency the same as 450Hz, higher than 450Hz, or lower than 450Hz. I really suggest drawing a picture to help sort this out.

A car sitting stationary at the side of the road watching the oncoming ambulance.

A car driving East at a speed of 20m/s. The car is behind the ambulance.

A car driving East at a speed of 15m/s. The car is ahead of the ambulance.

A car driving East at a speed of 25m/s. The car is behind the ambulance.

Explanation / Answer

here,

Taking East direction as positive and west as negative
by using
Nu = ( (V+Vo) / (V+Vs) )F-------------------------(1)

Where,
V = 343 m/s speed of sound in air
Vs = 20 m/s

Case A:
Vo = 0,So Eqn 1 will be,
Nu = ( (V+Vo) / (V+Vs) )F
Nu = (343/(343+20) )*450
Nu = 425.20 hz

CASE B:
Vo = 20,so Eqn 1 becomes
Nu = ( (V+Vo) / (V+Vs) )F
Nu = ((343+20) / (343+20))*450
Nu = 450 Hz

CASE C:
Vo = 15,so Eqn 1 becomes
Nu = ( (V+Vo) / (V+Vs) )F
Nu = ((343+15) / (343+20))*450
Nu = 443.80 Hz

CASE D:
Vo = 15,so Eqn 1 becomes
Nu = ( (V+Vo) / (V+Vs) )F
Nu = ((343+25) / (343+20))*450
Nu = 456.198 Hz

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