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January 29, 2015

January 29, 2015

Posted by **sarah** on Wednesday, November 10, 2010 at 9:02am.

What is the closest you can be to speaker B and be at a point of destructive interference?

- physics -
**bobpursley**, Wednesday, November 10, 2010 at 9:13amdraw the figure. draw a triangle short side from A, long side from B, other side A to B.

so the difference between the short side and the long side has to be an even multiple of 1/2 wavelength.

start with the wave equation

lambda= v/f

so long side-short side= n(v/2f)

do the degenerate triangle first, where short+long= AB (a point on AB)

nv/2f+nv/2f+v/2f=ab

or v/2f(2n+1)=ab

you know ab as 8m, so solve for n

then solve for short side length.

Now do the same thinking for some triangle .

Use the law of cosines to find short side, then minimize it with differential calculus.

You will find the answer, and discovering something magic about the angle from B, it gets minimized also.

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