Question

Standing at a crosswalk, you hear a frequency of 590 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 497 Hz. Determine the ambulance's speed from these observations. (Take the speed of sound to be 343 m/s.)

Answer 1

let the actual frequency of the ambulance be "f"

f' = frequency of the siren observed when the ambulance approach = 590 Hz

V = speed of sound = 343 m/s

v = speed of ambulance = ?

frequency observed when ambulance approach the listener at rest

f' = V f/(V - v) eq-1

f'' = frequency of the siren observed when the ambulance moves away = 497 Hz

V = speed of sound = 343 m/s

v = speed of ambulance = ?

frequency observed when ambulance moves away from the listener at rest

f'' = V f/(V + v) eq-2

dividing eq-1 by eq-2

f'/f'' = (V f/(V - v) ) ((V + v)/(Vf))

590/497 = (V + v)/(V - v)

590/497 = (343 + v)/(343 - v)

v = 29.35 m/s