Question

Two trucks have sirens that emit waves of the same frequency. As the trucks approach a person, the person hears a higher frequency from truck X than from truck Y. Which of the following statements about truck X can be correctly inferred from this information

I. It is traveling faster than truck Y

II. It is close to the person than the truck Y

III. It is speeding up, and truck Y is slowing down.

(A) I only

(B) III only

(C) I and II only

(D) II and III only

(E) I, II and III

Answer 1

The correct option is: (A) I only

Explanation:

Based on the Doppler effect, only speed matters. The faster a vehicle is moving, the closer together the sound waves get compressed and the higher the frequency. Take the case of a very fast vehicle traveling at the speed of sound; the compressions are all right on top of each other. So faster speed means closer compressions and higher frequencies. Choice I must be true because X is a higher frequency so must be going faster. Distance to the person affects the volume but not the pitch so choice II is wrong. III seems correct but its not. It doesn’t matter whether you are speeding up or slowing down, it only matters who is going faster. For example, suppose truck X was going 5 mph and speeding up while truck Y was going 50 mph and slowing down, this is an example of choice III but would not meet the requirement that X has a higher frequency because only actual speed matters, not what is happening to that speed.