Problem

You are standing against a wall opposite two speakers that are separated by 3.00 m, as sh...

You are standing against a wall opposite two speakers that are separated by 3.00 m, as shown in the figure. The two speakers begin emitting a 343-Hz tone in phase. Where along the far wall should you stand so that the sound from the speakers is as soft as possible? Be specific; how far away from a spot centered between the speakers will you be? The far wall is 120. m from the wall that has the speakers. (Assume the walls are good absorbers, and therefore, the contribution of reflections to the perceived sound is negligible.)

Solution 1

Step #1 of 6

THINK:

We have to find the spots of destructive interference along a far wall from the two speakers which are in phase. The distance between the speakers is and the distance between the speakers and far wall is. The frequency of the sound is and speed of the sound is.

Step #2 of 6

SKETCH:

Positions of the speakers and the person are shown in the figure given below.

Step #3 of 6

RESEARCH:

From above sketch the difference in the paths traveled by the two sound waves is

The condition for the destructive interference at the far wall is

For, it can be seen that

Therefore,

Here, y is distance of the point from the center of the wall, where the destructive interference takes place.

Step #4 of 6

SIMPLIFY:

The distance from the center of the far wall to the point of destructive interference is

Here,

Step #5 of 6

CALCULATE:

Wavelength of the sound,

For the first point of destructive interference,

Distance of the first point where destructive interference takes place:

Step #6 of 6

ROUND:

The answer is rounded to two significant figures.

Distance of the first point of destructive interference,

Solution 2

Step #1 of 6

THINK:

We have to find the spots of destructive interference along a far wall from the two speakers which are in phase. The distance between the speakers is and the distance between the speakers and far wall is. The frequency of the sound is and speed of the sound is.