You are standing against a wall opposite two speakers that are separated by 3.0m

Question

You are standing against a wall opposite two speakers that are separated by 3.0m. The two speakers begin emitting a 343Hz 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 120m 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.)

Explanation / Answer

This is an interference problem and one should stand at a point on the wall where the path difference between the waves reaching is /2 or an odd multiple of it so that there is destructive interference.

Wavelength of the wave= Speed of wave/frequency

= 343/343 m= 1m.

Let the distance along the wall be y from the centreline.

The path difference at that point= d*y/D. [D is distance from wall=120 m and d= distance between speakers]

This path difference should be /2 for destructive interference

d*y/D= /2

y=D*/(2*d)

=120*1/(2*3)

=20 m from the centre is the minimum distance

The other such point will be for path difference of 3/2

This will give a y=60 m.

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