The Shinkansen, the Japanese \"bullet train\" runs at high speed from Tokyo to N

Question

The Shinkansen, the Japanese "bullet train" runs at high speed from Tokyo to Nagoya. Riding on the Shinkansen, (and course having perfect pitch) you notice that the frequency of a crossing signal is 4500 Hz as you approach the signal. You know from the tourist guide book that all crossing signals in Japan emit a frequency of 3800 Hz. How fast is the Shinkansen traveling? After you pass the crossing signal, you notice the frequency appears to have changed. Calculate the frequency that you would observe as the train moves away from the crossing signal. If you detect the horn of the train to have a decibel level of 90 dB, what is the intensity of the sound at your location?

Explanation / Answer

a)
let

f = 3800 Hz

f' = 4500 Hz

velocity of sound, v = 343 m/s

velocity of obsorver, vo = ?

use Doppler's effect equation

f' = f*(v + vo)/v

f'*v/f = v + vo

==> vo = f'*v/f - v

= 4500*343/3800 - 343

= 63.2 m/s <<<<<<<<<<------------Answer

b) f'' = f*(v - vo)/v

= 3800*(343 - 63.2)/343

= 3100 Hz <<<<<<<<<<------------Answer

let I is Intensity of the sound.
we know, sound inetnsity level, beta = 10*log(I/Io)

90 = 10*log(I/Io)

9 = log(I/Io)

10^9 = I/Io

I = 10^9*Io

= 10^9*10^-12

= 10^-3 W/m^2 <<<<<<<<<<-----------Answer

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