A car travelling at constant speed passes by a stationary pe

A car travelling at constant speed passes by a stationary pedestrian as the car driver sounds the horn. As the car approaches the pedestrian she hears the horn sounding at 52 Hz. Once the car has driven past her, she hears the horn sounding at 15 Hz. Calculate the speed of the car, in m s1, to 2d.p.

Solution

we know, speed of sound, vo = 343 m/s

let f is the actual frequency of the sound produced by the car.

let v is the speed of the car.

when car approches,

f\' = f*vo/(vo - v)

52 = f*343/(343 - v) ----(1)

when car moves away,

f\'\' = f*vo/(vo + v)

15 = f*343/(343 + v) ---(2)

take equation (2)/equation(1)

15/52 = (343 - v)/(343 + v)

==> v = 189 m/s