Question

A high speed train is traveling at a speed of 44.7 m/s (100 mph) when the engineer sounds the 415 Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a person standing at a crossing when the train is (a) approaching and (b) leaving the crossing

Answer 1

Answer:

a) When the train is approaching the frequency is 477.19 Hz and the wavelenght is 0.719 m

b) When the train is leaving the crossing the frequency is 367.152 Hz and the wavelenght is 0.934 m

Explanation:

Given data:

v = speed of the train = 44.7 m/s

V = speed of the sound = 343 m/s

f = frequency of sound = 415 Hz

a) If the train is approaching, the frequency is:

$f_{ap} =f(\frac{V}{V-v} )=415(\frac{343}{343-44.7} )=477.19Hz$

The wavelength is:

$w=\frac{V}{f_{ap} } =\frac{343}{477.19} =0.719m$

b) If the train leaves the crossing, the frequency is:

$f_{le} =f(\frac{V}{V+v} )=415(\frac{343}{343+44.7} )=367.152Hz$

The wavelength is:

$w=\frac{V}{f_{le} } =\frac{343}{367.152} =0.934m$