Question

A train blowing the whistle moves with a constant velocity 'V' away from an observer standing on the platform. The ratio of the natural frequency of the whistle 'n' to the apparent frequency is 1.2 : 1. If the train is at rest and the observer moves away from it at the same velocity 'V', the ratio of 'n' to the apparent frequency is ______.

Options

• 1.52 : 1

• 0.51 : 1

• 2.05 : 1

• 1.25 : 1

Answer 1

A train blowing the whistle moves with a constant velocity 'V' away from an observer standing on the platform. The ratio of the natural frequency of the whistle 'n' to the apparent frequency is 1.2 : 1. If the train is at rest and the observer moves away from it at the same velocity 'V', the ratio of 'n' to the apparent frequency is 1.25 : 1.

Explanation:

In the 1st case, the apparent frequency is given by

`"n_1"="n"("V"_s)/("V"_s+"V")`

where V_s is the velocity of sound.

`therefore"n"/"n"_1=1.2=("V"_s+"V")/"V"_s`

∴ 1.2 V_s = V_s + V

∴ 1.2 V_s - V_s = V

V = 0.2 V_s

In the second case,

`"n"_2="n"(("V"_s-"V")/"V"_s)`

`therefore"n"/"n"_2=("V"_s)/("V"_s-"V")="V"_s/("V"_s-0.2  "V"_s)`

`=1/0.8=1.25`