Question

Two trains A and B simultaneously start moving along parallel tracks from a station along same direction. A starts with constant acceleration 2ms-1 from rest, which B with the same acceleration but with initial velocity of 40ms-1. 20 second after start, passenger of a hears whistle of B. If frequency of whistle is 1194 Hz and velocity of sound in air is 322ms-1, calculate frequency observed by the passenger.

Answer 1

Since, both the trains move in same direction with same acceleration, therefore, their relative acceleration is zero. Initial velocity if train A is zero while that of train B is 40 ms-1, therefore, train A or observer is behind the train B or source when whistle is heard by passenger of A. Let this sound be produced at time t .

Considering motion of train B (sound source) upto this instant,

When sound was produced, train B (source) was at a distance SB from initial point while observer receives this sound at t = 20sec and at distance SA from initial point. It means that sound waves travel distance SB - SA in air and take time (20 - t) to travel it.