Question

A light-rail commuter train blows its 200 Hz horn as it approaches a crossing. The speed of sound is 339 m/s. (a) An observer waiting at the crossing receives a frequency of 220 Hz. What is the speed of the train? m/s (b) What frequency does the observer receive as the train moves away? Hz

Answer 1

a) 30.82 m/s

b) 183.33 Hz

Step-by-step explanation:

a)

V = speed of the sound = 339 m/s

v = speed of the train = ?

f' = observed frequency by the observer = 220 Hz

f = actual frequency of the observer = 200 Hz

using the equation

`f' = (fV)/(V - v)`

`220 = ((200)(339))/(339 - v)`

v = 30.82 m/s

b)

V = speed of the sound = 339 m/s

v = speed of the train = 30.82 m/s

f'' = observed frequency by the observer as train moves away = ?

f = actual frequency of the observer = 200 Hz

using the equation

`f'' = (fV)/(V + v)`

`f'' = ((200)(339))/(339 + 30.82)`

f'' = 183.33 Hz