Question

When a train approaches a stationary observer, the apparent frequency of the whistle is $n'$ and when the same train recedes away from the observer, the apparent frequency is $n''.$ Then the apparent frequency $n$ when the observer moves with the train is

• A. $n=\frac{n' +n}{2}$
• B. $n=\sqrt{n' n''}$
• C. $n=\frac{2 n' n''}{n' +n''}$
• D. $n=\frac{2 n' n''}{n'-n''}$

Answer 1

Answer: (C)

As, $n'=\frac{v \pi}{v-v_{s}}$ and $n''=\frac{v n}{v+ v_{s}}$
$\therefore \frac{n}{n'}=1-\frac{v_{5}}{v},$
$\frac{n}{n''}=1+\frac{v_{s}}{v}$
Adding the two, we get
$\frac{n}{n'}+\frac{n}{n''}=2$
$\therefore n=\frac{2 n' n''}{n' +n''}$