The security alarm on a parked car goes off and produces a frequency of 758 Hz. The speed of sound is 343 m/s. As you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 68.5 Hz. At what speed are you driving?
Given :
f0 = frequency emitted = 758
vo = velocity of receiver
c = velocity of sound = 343 m/s
the frequency heard when you move towards a sound source at rest
is
f = f0*(1+ vr/c) with )
the frequency you hear when moving away from the sound source
is
f = f0*(1 - vr/c)
the difference between both frequencies is 68.5 Hz.
68.5 = f0(1 + vr/c) - v0(1 - vr/c)
68.5 = f0(1 + vr/c - (1 - vr/c))
68.5 = f0(vr/c + vr/c)
2vr/c = 68.5/f0
vr = 68.5c/(2f0)
vr = 68.5*343/(2*758)
vr = 15.498 m/s
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