Question

A train moves towards a stationary observer with a speed of $34\text{m/s}$. The train sounds a whistle and its frequency registered by the observer is $f_1$ . If the train speed is reduced to $17\text{m/s}$, the frequency registered is $f_2$. If the speed of sound is $340\text{m/s}$, then the ratio $\frac{f_1}{f_2}$ is

• A. $\frac{1}{2}$
• B. $2$
• C. $\frac{18}{19}$
• D. $\frac{19}{18}$

Answer 1

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

Let $f$ be the actual frequency
Case 1:
Speed of observer, $v_0=0$
Speed of source, $v_s=34\text{m/s}$
Apparent frequency observed by observer,
$f_1=\left(\frac{v\pm v_0}{v\pm v_s}\right)f$
$f_1=\left(\frac{340}{340-34}\right)f$
$f_1=\frac{10}{9}f$

Case 2:
Speed of observer, $v_0=0$
Speed of source, $v_s=17\text{m/s}$
Apparent frequency observed by observer,
$f_2=\left(\frac{v\pm v_0}{v\pm v_s}\right)f$
$f_2=\left(\frac{340}{340-17}\right)f$
$f_2=\frac{20}{19}f$
$\frac{f_1}{f_2}=\frac{19}{18}$