Q: A train moves towards a stationary observer with speed 34 m/s. the train sounds a whistle and its frequency registered by the observer is f_{1}. If the trainâ€™s speed is reduced to 17 m/s, the frequency registered is f_{2}. If the speed of sound is 340 m/s then the ration f_{1}/f_{2} is

(a) 18/19

(b) 1/2

(c) 2

(d) 19/18

Ans: (d)

Sol: Using formula ,

$\large f’ = \frac{v-v_o}{v-v_s}\times f$

Here observer is at rest ,

$\large f’ = \frac{v}{v-v_s}\times f$

In first case ,

$\large f_1 = \frac{340}{340 – 34}\times f$ …(i)

In second case ,

$\large f_2 = \frac{340}{340 – 17}\times f$ …(ii)

on dividing (i) by (ii)

$\large \frac{f_1}{f_2} = \frac{19}{18}$