Two trains are moving towards each other at speeds of `72kmh^-1` and `54 kmh^-1` relative to the ground. The first train sounds a whistle of frequency 600 Hz. Find the frequency of the whistle as heard by a passenger in the second train a. before the trains meet and b. after the trains have crossed each other. The speed of sound in air is `340 ms^-1`

Explanation

The speed of the first train `=72kmh^-1` =20ms^-1` and that of the second `=54kmh^-1=15ms^-1`. a. Here both source and the observer move with respect to the medium. Before the trains meet, the source is going towards the observer and the observer is also going towards the source. The apparent frequency heard by the observe will be
`v'=(+u_@)/(v-u_s)v`
`(340+15)/(340-20)xx600Hz=666Hz.`
b. After the trains have crossed each other, the source goes away from the observer and the observer goes away from source. The frequency heard by the observe is therefore
`v''=(v-u_@)/(u+u_s)`
`=(340-15)/(340+20)xx600Hz-542Hz`