When a train is approaching the observer, the frequency of the whistle is 100 cps. When it has passed observer, it is 50 cps. Calculate the frequncy when the observer moves with the train.

Explanation

When the source (the train) moves towards the observer, the apparent frequency is
`f'=(v)/(v-v_S)f` .. (i)
When the source is moving away, the apparent frequency is
`f'=(v)/(v+v_S)f` ..(ii)
`(f')/(f'')=(v+v_S)/(v-v_S)`
or `(100)/(50)=(2)/(1)=(((v)/(v_S)+1))/(((v)/(v_S)-1))`
or `(v)/(v_S)=3` ...(iii)
When the observer moves with the train there is no relative motion between the source and the observer and hence he will listen the true frequency f. Substituting (iii) in (i) we get
`100=(3)/(2)f`
or `f=(200)/(3)=66.6Hz`