An ambulance with a siren emitting a whine at 1790 Hz overta

An ambulance with a siren emitting a whine at 1790 Hz overtakes and passes a cyclist pedaling a bike at 2.28 m/s. After being passed, the cyclist hears a frequency of 1779 Hz. How fast is the ambulance moving? (Take the speed of sound in air to be 343 m/s.)

Solution

v = 343 m/s, v_D = 2.28 m/s

f\' = 1779 hz, f = 1790 hz

f\' = f [v + v_D / v + v_s]

v_s = f / f\' [v + v_D] - v

= 1790 / 1779 [343 + 2.28] - 343

= 4.41 m/s