Question

A train blowing its whistle moves with a constant velocity $u$ away from the observer on the ground. The ratio of the actual frequency of the whistle to that measured by the observer is found to be $1.2$. If the train is at rest and the observer moves away from it at the same velocity, the ratio would be given by:

• A. $0.51$
• B. $1.25$
• C. $1.52$
• D. $2.05$

Answer 1

The correct option is B $1.25$

When the train is moving away, then the apparent frequency will be:
$n_1=\left(\frac{u}{u+u_s}\right)n$
Given: $\frac{n}{n_1}=1.2$

So, using this we can get: $\frac{u_s}{u}=0.2$
Now when the observer is moving away, then the apparent frequency will be: $n_2=\left(\frac{u-u_o}{u}\right)n$

Here, $u_o=u_s$

Solving, it we will get: $\frac{n}{n_2}=1.25$.