Question

The security alarm on a parked car goes off and produces a frequency of 1370 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 147 Hz. At what speed are you driving?

Answer 1

here,

the frequency heard when you move towards a sound source at rest is
f = f0*(1+ vr/c) with

f0 = frequency emitted,

vo = velocity of receiver,

c = velocity of sound)

the frequency you hear when moving away from the sound source is
f = f0*(1 - vr/c)

the difference between both frequencies is 147 Hz.

147 = f0(1 + vr/c) - v0(1 - vr/c)

147 = f0(1 + vr/c - (1 - vr/c))

147 = f0(vr/c + vr/c)

2vr/c = 147/f0

vr = 147 * c/(2f0)

vr = 147 * 343/(2*1370)

vr = 18.4 m/s