Question

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 12 m to the right of speaker A. The frequency of the waves emitted by each speaker is 686 Hz. Sound velocity is 343 m/s.
You are standing between the speakers, along the line connecting them, and are at a point of constructive interference.

How far must you walk toward speaker B to move to a point of destructive interference?
How far must you walk toward speaker B to move to another point of constructive interference?

Answer 1

DRAW A PICTURE
The way I am looking at it:
speaker at x = -6
speaker at x = +6
wave from left at x = -6 moves right
y = sin (w t - 2 pi x/L)
wave from right at x = + 6 moves left
y = sin (w t + 2 pi x/L)

at x
y=sin(wt-2pi x/L)+sin(wt+2pi x/L)
= 2sin(wt)*cos(2 pi x/L)
This is your plain old "standing wave"
for destructive
cos 2pi x/L = 0
cos = 0 when 2 pi x/L = pi/2
or x/L = 1/4
then move another quarter to x/L = 1/2 to get cos = -1 for max again
now we need to know what is L of course
L = c T = c/f
= 343 /686 = .5 :) easy