Question

A train is approaching a signal tower at a speed of 40m/s. The train engineer sounds the 1000-Hz whistle, while a switchman in the tower responds by sounding 1200-Hz siren. THe air still and the speed is 340m/s. What is the frequency of the train whistle tone that is heard by the switchman?
300/340x1000Hz
380/340x1000Hz
340/300x1000Hz
1000Hz
340/380x1000Hz

Answer 1

v = speed of the source of sound or the train towards the listener or switchman = 40 m/s

V = actual speed of sound = 340 m/s

f = actual frequency of sound as emitted from source or the train = 1000 Hz

f' = frequency as observed by the listener or by switchman = ?

Using Doppler's law , frequency observed by a listener from a source moving towards it is given as

f' = V f /(V - v)

inserting the values

f' = 340 x 1000 /(340 - 40)

f' = 340 x 1000/300