You are walking around a large open field. The only objects nearby are two ident

Question

You are walking around a large open field. The only objects nearby are two identical speakers set some distance apart, which are both producing sound, in unison, with a wavelength of 4 m. As you wander around the field, you notice that at certain locations, the sound you hear is surprisingly loud, while at others it seems unusually quiet. You conclude that you are observing the effects of interference between the two sources of sound waves. For each of the locations given below, indicate what sort of interference would occur at that point. Constructive interferenceDestructive interference In between 9 m from one speaker 20 m from each spea and 13 m from the other 11 m from one speaker and 14 m from the other 10 m from one speaker and 8 m from the other 16 m from one speaker and 24 m from the other 13 m from one speaker 13 m from one spea and 18 m from the other and 19 m from the other

Explanation / Answer

1) Phi = (2 pi/4 m)( 20 - 20 ) = 0

Constructive interference

2) Phi = (2 pi/4 m)( 16 - 24 ) = -4 pi

Constructive interference

3) Phi = (2 pi/4 m)( 9 - 13 ) = -2 pi

Constructive interference

4) Phi = (2 pi/4 m)(10 - 8 ) = pi

Destructive interference

5) Phi = (2 pi/4 m)(13 - 19 ) = -3 pi

Distructive interference

6) Phi = (2 pi/4 m)(11 - 14) = -(3/2) pi

In between

7) Phi = (2 pi/4 m)(13 - 18) = - (5/2) pi

In between.

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