Question

An ambulance has an insert horn whose tones carry the frequencies 440 Hz and 587 Hz. He overtakes a cyclist waiting at a traffic light. Then the cyclist hears a tone sequence in which the higher frequency is 565 Hz. How fast did the ambulance drive? Expect a speed of sound of 340 m / s.

Answer 1

Given that Ambulance overtakes the cyclist,

So Using doppler effect

When Source is moving away from an observer at rest, then observed frequency will be

f1 = f0*V/(V + Vs)

V = Speed of sound = 340 m/sec

Vs = Speed of Source (Ambulance) = ?

f0 = 587 Hz

f1 = 565 Hz (Given that this is higher frequency we choose f0 as 587 Hz)

Now Using these values:

565 Hz = 587 Hz*(343)/(343 + Vs)

Vs = (587*343 - 565*343)/565

Vs = Speed of ambulance = 13.35 m/sec

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