Approaching a platform at a speed of 54 km/h , a train sounds a whistle. An observer on the platform measures its frequency to be 1620 Hz . The train passes the platform without slowing down while keeping the whistle on. What frequency will the observer hear after the train has crossed the platform? The speed of sound in air is 332 m/s .

Step-by-step solution

Speed of the train, v_s = 54 km/h = 54 5 18 m/s = 15 m/s Apparent frequency during approach, f₁ = 1620 Hz Speed of sound, v = 332 m/s By Doppler's effect, the apparent frequency when the train approaches the stationary observer is given by: f₁ = f₀ ( v v - v_s ) 1620 = f₀ ( 332 332 - 15 ) = f₀ ( 332 317 ) f₀ = 1620 317 332 When the train crosses the platform and moves away, the apparent frequency heard by the observer is: f₂ = f₀ ( v v + v_s ) Substituting the value of f₀ : f₂ = 1620 ( 317 332 ) ( 332 332 + 15 ) f₂