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Answer :
A stationary police car has its siren going at a frequency of 450 Hz, the magnitude of the maximum change in frequency heard by the moving car driver is approximately 39.4 Hz.
The Doppler effect formula for frequency shift observed by a moving observer is given by:
[tex]\(\Delta f = f' - f \\\\= f \left( \frac{v}{v + v_o} - 1 \right)\),[/tex]
where:
[tex]\(\Delta f\)[/tex] is the change in frequency,
f is the source frequency (450 Hz in this case),
v is the speed of sound in air (343 m/s),
[tex]\(v_o\)[/tex] is the speed of the moving observer (15.0 m/s).
Substitute the values:
[tex]\(\Delta f = 450 \left( \dfrac{343}{343 + 15.0} - 1 \right)\\\\ \approx 39.4 \, \text{Hz}\).[/tex]
Thus, the magnitude of the maximum change in frequency heard by the moving car driver is approximately [tex]\(39.4 \, \text{Hz}\)[/tex].
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