Question

A train approaching a platform at a speed of 54 km/h sounds a whistle. An observer on the platform finds its frequency to be 1620 Hz. The train passes the platform keeping the whistle on and without slowing down. What frequency will the observer hear after the train has crossed the platform? The speed of sound in air = 332 m/*.

Answer 1

The speed of sound in air, V =332 m/. The speed of the source, u = 54 km/h = 54000/3600 m/ = 15 m/*. Apparent frequency heard by the observer when the source is approaching, ν' = 1620 Hz. Let the actual frequency of the source = ν, then ν' = Vν/(V-u)

→1620 = 332ν/(332-15) =332ν/317

→ν = 1620*317/332 Hz

When the train has crossed the platform the source is receding, hence the apparent frequency now,

ν" = Vν/(332+15)=332ν/347

=(332/347)(1620317/332)

{Putting the value of ν}

=1620*317/347 Hz

=1480 Hz