Question

While standing near a bus stop, a student hears a distant horn beeping. The frequency emitted by the horn is 440 Hz. The bus is traveling at 20.0 m/s, and the speed of sound is 330 m/s. What frequency will the student hear at each point in the bus's motion?

A. 468 Hz while approaching, 440 Hz through the crossing, 415 Hz while receding
B. 415 Hz while approaching, 440 Hz through the crossing, 468 Hz while receding
C. 440 Hz while approaching, 415 Hz through the crossing, 400 Hz while receding
D. 505 Hz while approaching, 440 Hz through the crossing, 438 Hz while receding

Answer 1

A. 468 Hz while approaching, 440 Hz through the crossing, 415 Hz while receding

Step-by-step explanation:

When bus is approaching the stand where boy is standing then the frequency is given as

now we know that

`f_0 = 440 Hz`

`v = 330 m/s`

`v_b = 20 m/s`

frequency is given by

`f_1 = f_0 (v)/(v - v_b)`

now plug in the data in the equation

`f_1 = 440 * (330)/(330 - 20)`

`f_1 = 468 Hz`

Now when bus is moving away from the bus stop then frequency is given as

`f_2 = f_0 (v)/(v + v_b)`

`f_2 = 440 * (330)/(330 + 20)`

`f_2 = 415 Hz`

so here correct answer would be

A. 468 Hz while approaching, 440 Hz through the crossing, 415 Hz while receding