Question

A bystander hears a siren vary in frequency from 582 Hz to 394 Hz as a fire truck approaches, passes by, and moves away on a straight street. What is the speed of the truck? (Take the speed of sound in air to be 343 m/s.)

Answer 1

f = actual frequency

v = speed of truck

V = speed of sound = 343 m/s

f' = frequency heard while approaching = 582 Hz

f'' = frequency heard while truck move away = 394 Hz

while approaching , frequency heard is given as

f' = vf/(V-v)

582 = vf/(343-v)                         eq-1

while moving , frequency heard is given as

f' = vf/(V-v)

394 = vf/(343+v)                         eq-2

dividing eq-1 by eq-2

582/394 = (343 + v) /(343 - v)

v = 66.1 m/s