The frequency produced by the siren is 631.12 Hz
The variation in frequency when a source of sound moves relative to an observer is determined by the doppler effect.
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
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
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