Question

A freight train is traveling at 30.0 m/s relative to the ground in still air. The temperature is 20° C. The frequency of the note emitted by the train whistle is 262 Hz. A car passes by the train on a road right next to the train track.

(a) What frequency f1 is heard by a driver of a car moving at 18.0 m/s relative to the ground in a direction opposite to the train and approaching it?

(b) What frequency f2 is heard by a driver of a car moving at 18.0 m/s relative to the ground in a direction opposite to the train and receding from it?

(c) A week later, the same car passes the same train. The situation is completely identical, except the temperature is only 15° C. Is the change in frequency as the car passes the train ( f1 – f2 ) greater on the warmer day or the cooler day?
Justify your answer.

Answer 1

speed of train = vt = 30 m/s

speed of the car =vc = 18 m/s

speed of sound v = 343 m/s

frequency emitted f0 = 262 Hz

(a)

frequency heard f1 = f0*(v+vc)/(v-vt)

f1 = 262*(343+18)/(343-30) = 302.2 Hz

(b)

frequency heard f2 = f0*(v-vc)/(v+vt)

f2 = 262*(343-18)/(343+30) = 228.3 Hz

(c)

at 20 oC

f1 - f2 = 302.2-228.3 = 73.9 Hz

at 15 degrees celsius

V = 340 m/s

f1 = 262*(340+18)/(340-30) = 302.6

f2 = 262*(340-18)/(340+30) = 228 Hz

f1 - f2 = 302.6-228 = 74.6 Hz

f1-f2 is greater on cooler day