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

Answer:

a) 30.82 m/s

b)  183.33 Hz

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

$f' = \frac{fV}{V - v}$

$220 = \frac{(200)(339)}{339 - v}$

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

$f'' = \frac{fV}{V + v}$

$f'' = \frac{(200)(339)}{339 + 30.82}$

f'' = 183.33 Hz