Question

Two trains $A$ and $B$ are moving with speeds $20m/s$ and $30m/s$ respectively in the same direction on the same straight track, with $B$ ahead of $A$. The engines are at the front ends. The engine of train $A$ blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800Hz$ to $f_2=1120Hz$ as shown in the figure. The speed in the frequency (highest frequency lowest frequency) is thus $320Hz$. The speed of sound in still air is $340m/s$.

The speed of sound of the whistle is :

• A. $340m/s$ for passengers in $A$ and $310m/s$ for passenger in $B$
• B. $360m/s$ for passengers in $A$ and $330m/s$ for passenger in $B$
• C. $310m/s$ for passengers in $A$ and $360m/s$ for passenger in $B$
• D. $340m/s$ for passengers in both the trains

Answer 1

The correct option is B $360m/s$ for passengers in $A$ and $330m/s$ for passenger in $B$

Applying concepts of relativity

relative velocity $=30-20$

$=10m/s$.

Speed of second of whistle for passenger in $A$

$340+20$

$=360m/s$.

Speed of second of whistle for passenger in $B$

$=340-$ relative velocity

$=340-10$

$=330m/s$.