A train moves towards a stationary observer with speed $34 \mathrm{~m} / \mathrm{s}$. The train sounds a whistle and its frequency registered by the observer is $\mathrm{f}_{1}$. If the speed of the train is reduced to $17 \mathrm{~m} / \mathrm{s}$, the frequency registered is $\mathrm{f}_{2}$. If speed of sound is $340 \mathrm{~m} / \mathrm{s}$, then the ratio $f_{1} / f_{2}$ is:

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Waves & Sound

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 speed of the train is reduced to

17 m / s

, the frequency registered is

f_{2}

. If speed of sound is

340 m / s

, then the ratio

f_{1} / f_{2}

is:

Answer: (B)

For a source approaching a stationary observer the registered frequency is

f = f_{0} \frac{v}{v - v _{s}}

. At

34

m/s,

f_{1} = f_{0} \frac{340}{306}

, and at

17

m/s,

f_{2} = f_{0} \frac{340}{323}

, so

\frac{f _{1}}{f _{2}} = \frac{323}{306}

. Cancelling the common factor

17

, since

323 = 19 \times 17

and

306 = 18 \times 17

, leaves

\frac{19}{18}

. Slowing the train lowers the pitch it presents, so

f_{1} > f_{2}

as the ratio above one confirms.

JEE Main · 2019 · 10 Jan 2019 · Shift 1 · Single correct option