Question

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 f1. If the train's speed is reduced to 17 m/s, and it moves away from observer the frequency registered is f2. If the speed of sound is 340 m/s then the ratio f1/f2 is -

• A. $\frac{18}{19}$
• B. $\frac{7}{9}$
• C. no option
• D. $\frac{19}{18}$

Answer 1

The correct option is D $\frac{19}{18}$

$n_{app}=n_0\left\{\frac{\theta -{\theta }_v}{v-v_s}\right\}$
$=n_0\left\{\frac{340-0}{340-34}\right\}$
$=n_0\left\{\frac{10}{9}\right\}=\frac{10n_0}{9}$
$n_{app}=n_0\left\{\frac{\theta -{\theta }_v}{v-v_{\lambda }}\right\}=n_0\left(\frac{340}{340+17}\right)$
$n_0\times \frac{20}{21}$
$f_1=\frac{10n_0}{9}$ $\frac{f_1}{f_2}=\frac{\frac{10}{9}}{\frac{20}{21}}=\frac{1}{2}\times \frac{21}{9}$
$f_2=\frac{20n_0}{21}$ $=\frac{21}{18}=\frac{7}{9}$