A truck moving at 45 m/s passes a police car moving at 36 m/s in the opposite direction. if the frequency of the siren is 500 Hz relative to the police car, what is the frequency heard by an observer in the truck after the police car passes the truck

Answer: observed frequency (f') = 511.97Hz

Explanation: when there is a relative motion between an observer and a sound source, the frequency of sound wave perceived by the observer is different from the frequency of originally sent out by the sound source.

This is called Doppler effect and given mathematically below as

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

f' = observed frequency

v = speed of sound in air = 340m/s

v' = velocity of observer = 45m/s

vs = velocity of source relative to observer = - 36m/s (the negative sign came as a result of the fact that the velocity of the source is in opposite direction to the velocity of the observer)

f = original frequency of sound source = 500Hz

f' = (340 + 45) / {340 - (-36) } * 500

f' = 385 / (340 + 36) * 500

f' = 385 / 376 * 500

f' = 1.0239 * 500

f' = 511.97Hz