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)

According to Doppler effect the the pitch of a sound change due the motion of source is given by:
$\overline{ n }= n \frac{ v - v _{0}}{ v - v _{ s }}$
Here, $v_{ s }$ and $v _{0}$ are the velocity of the sound source and observer and $v =330\, m / s$ and $\overline{ n } / n = 9/8$.
Lets assume the velocity of both the the trains are $\bar{v}$.
Using the above formula:
$\overline{ n } / n =9 / 8=\frac{ v -(-\overline{ v })}{ v -\overline{ v }}$.
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 $20\, m / s$.