A train approaches a tunnel in a vertical cliff perpendicular to the rail road tracks. It sounds its horn with a frequency of 250 Hz. The speed of the train is 100 km/h and the speed of sound is 340m/s.

a. What is the frequency of sound heard by an observer standing at the entrance of the Tunnel?

b. What is the frequency of sound reflected by the cliff and heard by an engineer on the train?

a. The detected frequency is Hz.

a. First we need to make a change of units for the speed of the train. The speed of the train is

Since the sound source (the train) is approaching a stationary observer, the observed frequency is

Answer

b. Now the train is the observer and the cliff is the source. The new observed frequency is

Since the observer is moving toward the source, the frequency has increased.

b. The detected frequency is Hz.

2-7 The Doppler effect

Example 2