Question

A train approaching a hill at a speed of 40 km/hr sounds a whistle of frequency 600 Hz when it is at a distance of 1 km from a hill. A wind with a speed of 40 km/hr is blowing in the direction of motion of the train. Find the frequency of the whistle as heard by an observer on the hill.

Answer 1

speed of sound in air is c and as the air is also moving the velocity of sound is $c+v_a$ where $v_a$ is the speed of air

therefore the apparent frequency heard by the observer

$f_2=\frac{v}{v-v_s}f=\frac{c+40}{c+40-v_s}f=\frac{1240}{1240-40}\times 600=620Hz$