Question

The Bullet Train The Shinkansen, the Japanese "bullet" train, runs at high speed from Tokyo to Nagoya. Riding on the Shinkansen, you notice that the frequency of a crossing signal changes markedly as you pass the crossing. As you approach the crossing, the frequency you hear is f; as you recede from the crossing the frequency you hear is 2f/3.What is the speed of the train?

Answer 1

Answer:

68.6 m/s

Explanation:

v = Speed of sound in air = 343 m/s

u = Speed of train

$f_1$ = Actual frequency

From the Doppler effect we have the observed frequency as

When the train is approaching

$f=f_1\frac{v+u}{v}$

When the train is receeding

$\frac{2f}{3}=f_1\frac{v-u}{v}$

Dividing the above equations we have

$\frac{f}{\frac{2f}{3}}=\frac{f_1\frac{v+u}{v}}{f_1\frac{v-u}{v}}\\\Rightarrow \frac{3}{2}=\frac{v+u}{v-u}\\\Rightarrow 3v-3u=2v+2u\\\Rightarrow v=5u\\\Rightarrow u=\frac{v}{5}\\\Rightarrow u=\frac{343}{5}\\\Rightarrow u=68.6\ m/s$

The speed of the train is 68.6 m/s