 #1
 27
 0
Homework Statement:
 Two speakers A and B are 3.50 m apart, and each one is emitting a frequency of 444 Hz. However, because of signal delays in the cables, speaker A is onefourth of a period ahead of speaker B. For points far from the speakers, find all the angles relative to the centerline at which the sound from these speakers cancels. Include angles on both sides of the centerline. The speed of sound is 340 m/s.
Relevant Equations:

v = f(lambda)
dsin(theta) = (m+ 1/2)(lambda)
I already have the solution in front of me, I am wondering why there is a difference in the formula for path difference. I've attached the problem as well to show the Figure.
What I am struggling to grasp is why the path difference for the angles closer to A is dsin(Θ) = (m+1/4)λ while the path difference for the angles closer to B are dsin(Θ) = (m + 3/4)λ. I know that the phase shift for destructive interference has to be 1/2, but why does it change differently closer to the source with the phase shift and differently farther away from it?
Any help is appreciated!
What I am struggling to grasp is why the path difference for the angles closer to A is dsin(Θ) = (m+1/4)λ while the path difference for the angles closer to B are dsin(Θ) = (m + 3/4)λ. I know that the phase shift for destructive interference has to be 1/2, but why does it change differently closer to the source with the phase shift and differently farther away from it?
Any help is appreciated!
Attachments

103.1 KB Views: 64