Question

A loudspeaker at the front of a room and an identical loudspeaker at the rear of the room are being driven at the same frequency. As a student walks at a uniform rate from the back of the room to the front, she hears a single tone at 300 Hz repeatedly becoming louder and softer. The speed of sound is 343 m/s. The room is 11m wide and 7m deep.

A. calculate the distance she will need to walk toward the front of the room before she hears the first point of constructive interference.

B. How many total points of constructive interference will she pass on her way to the front of the room?

Answer 1

Answer A)

There are two identical loudspeakers placed at the opposite ends of the room.

Let us consider that the the distance between two loudspeakers is 11 m.

The two sound waves are travelling in opposite direction.let us consider that the girl started moving from the back side of the room towards the front side. At the middle of the room, the girl is at equal distance from the both the loudspeakers.

Suppose R1 be the distance of the girl from the front loudspeaker and R2 be the distance of the girl from the back loudspeaker, then the for the constructive interfernce,

R1-R2=0

That is at the middle of this distance one can hear first point of constructive intereference.