An ambulance is traveling East at 20m/s. The siren emits a fixed frequency of 31

Question

An ambulance is traveling East at 20m/s. The siren emits a fixed frequency of 310Hz. 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 310Hz, higher than 310Hz, or lower than 310Hz. I really suggest drawing a picture to help sort this out.
Higher Lower Same  A car driving West at a speed of 15m/s. The car is moving towards the ambulance.
Higher Lower Same  A car driving East at a speed of 20m/s. The car is in front of the ambulance.
Higher Lower Same  A car sitting stationary at the side of the road watching the oncoming ambulance.
Higher Lower Same  A car driving East at a speed of 25m/s. The car is ahead of the ambulance.

Explanation / Answer

a)

VL = speed of listener = 15 m/s

Vs = speed of source = 20 m/s

f = actual frequency = 310 Hz

Since Source (ambulance) and listener(car ) are moving towards each other, the apparent frequency is given as

f' = (V + VL) f / (V - Vs) = (343 + 15) (310) / (343 - 20) = 343.6 hz

so higher

b)

VL = speed of listener = 15 m/s

Vs = speed of source = 20 m/s

f = actual frequency = 310 Hz

Since Source (ambulance) and listener(car ) are moving in the same direction at same speed , hence

f' = f = 310

so Same

c)

VL = speed of listener = 0 m/s

Vs = speed of source = 20 m/s

f = actual frequency = 310 Hz

Since Source (ambulance) is at rest and listener(car ) is coming towards the source

f' = Vf/(V - Vs) = 343 x 310 / (343 - 20) = 329 Hz

so Higher

d)

VL = speed of listener = 25 m/s

Vs = speed of source = 20 m/s

f = actual frequency = 310 Hz

Since listener is moving away from source , hence frequency heard will be lower

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