Question

A fire truck emits an 1080 Hz siren. As the truck approaches an observer on the sidewalk, he perceives the frequency of the siren to be 1150 Hz. Approximately what frequency does he hear after the truck passes and is moving away? Assume the truck's velocity remains constant, and that the velocity of sound in air is 340 m/s.

Answer 1

For this above equation there's a formula of both the source and observer are moving.

F ' = [( c - Vo) / (c - Vs) ] Fo

Fo is actual frequency. Here it is 1080 Hz

F' = observed frequency

C = Velocity of sound in air, 340 m/s

Vo = velocity of observer

Vs = velocity of source( truck siren)

Case Ist when truck is coming near

F ' = [( c - Vo) / (c - Vs) ] Fo

F' = observed frequency given in case 1st = 1150Hz

Vo = 0 as observer is at rest at side walk.

Here we will find velocity of source

1150 = [ ( 340 -0 ) /(340 - Vs) ]*1080

After calculating

Vs = 20.7 m/s

Case 2 nd when source is moving away

F ' = [( c - Vo) / (c - Vs) ] Fo

Foe this case Vs = - 20.7 m/s as source is moving away that's why sign changes due to change of direction.

F' = [( 340 - 0) /(340 -(-20.7) )]* 1080

F' = 1018.02 Hz