Question

Two trains move towards each other with the same speed. The speed of sound is 340 m/s. If the height of the tone of the whistle of one of them heard on the other changes to 9/8 times, then the speed of each train should be

• A. 20 m/s
• B. 2 m/s
• C. 200 m/s
• D. 2000 m/s

Answer 1

Answer: (A)

20 m/s

Answer 2

According to Doppler effect the the pitch of a sound change due the motion of source is given by:
$\bar{ n }= n \frac{ v - v _{0}}{ v - v _{ s }}$
Here, $v _{ s }$ and $v _{0}$ are the velocity of the sound source and observer and $v =330 m / s$ and $\bar{ n } / n =9 / 8$.
Lets assume the velocity of both the the trains are $\bar{v}$.
Using the above formula:
$\bar{ n } / n =9 / 8=\frac{ v -(-\bar{ v })}{ v -\bar{ v }}$.
The negative sign used for the opposite direction movement of the trains.
Using all the known values we can get the velocity of the trains are $20\,m/s$.