Question

An emergency vehicle blowing its siren is moving

Answer 1

The frequency produced by the siren is 631.12 Hz

Doppler effect

The variation in frequency when a source of sound moves relative to an observer is determined by the doppler effect.

Frequency of observer

So, the frequency of the observer  f' = (v ± v')f/(v ± v") where

f' = 590 Hz

f = frequency of source or siren ,

v = speed of sound = 330 m/s,

v' = speed of observer = 0 m/s (since you are stationary) and

v" = speed of source = 23 m/s

Since the source moves away from the detector, the sign in the denominator is positive and v' = 0 m/s

So, f' = (v + 0)f/(v + v")

f' = vf/(v + v")

Since, we require the frequency of the source, make f subject of the formula, we have

Frequency of siren

f = (v + v")f'/v

Substituting the values of the variables into the equation, we have

f = (v + v")f'/v

f' = (330 m/s + 23 m/s)  × 590 Hz/330 m/s

f' = 353 m/s × 590 Hz/330 m/s

f' = 208270 m/sHz/330 m/s

f' = 631.12 Hz

The frequency produced by the siren is 631.12 Hz

Learn more about doppler effect here:

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