Question

What will be the percentage difference between the
frequency of the sound heard by an observer and the
actual frequency of the whistle of a train approaching at
a speed of 100 m.s- towards the observer? Velocity of
sound in air = 330 m.s-1.​

Answer 1

The Percentage difference in the frequency = 43.38%

Let f be the original frequency of the whistle of the train and f' be the frequency of the whistle as heard by the stationary observer .

v = 100 m/s = speed of the train and the velocity of sound in air = 330 m/s

Using the Doppler's effect equation to find the relation -

f' = f × (velocity w.r.t listener / velocity w.r.t source)

velocity w.r.t listener = velocity of sound = 330 m/s

velocity w.r.t source = velocity of sound - velocity of source = 330 - 100 = 230 m/s

f' = f ×(330/230)

f' = 33f/23

% Difference between the frequency= ((33f/23)-f)/f × 100

=> 1000/23

=> 43.38%