Standing at a crosswalk, you hear a frequency of 580 Hz from the siren of an app

Question

Standing at a crosswalk, you hear a frequency of 580 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 509 Hz. Determine the ambulance's speed from these observations. (Take the speed of sound to be 343 m/s.) (Please provide numerical answer in m/s)

Explanation / Answer

In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency f and emitted frequency fo is given by: f =[{v + v(r)}/{v + v(s)}] x fo where v is the velocity of waves in the medium v(r) is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source. v(s) is the velocity of the source relative to the medium; positive if the source is moving away from the receiver. The frequency is decreased if either is moving away from the other. Let the velocity of ambulance is v(s) m/s :- =>580 = [343/{343-v(s)}] x fo --------------(i) =>409 = [343/{343+v(s)}] x fo --------------(ii) By (i)/(ii):- =>580/409 = {343+v(s)}/{343-v(s)} =>1.14 x {343-v(s)} = {343+v(s)} =>2.14 x v(s) = 343 x 0.14 =>v(s) = 22.44 m/s

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