Finding wavelength of sound waves

[SilentBlade91]

Homework Statement

The two speakers are producing identical sound waves. The solid lines represent constructive interference regions and the dashed lines represent destructive interference regions. The point labeled 4 is 1228.5 m from the bottom speaker and 1618.5 m from the top speaker.
What is the wavelength of the sound waves?

Homework Equations

x-x=wavelength

The Attempt at a Solution

1618.5m-1228.5m=390m not correct
I wasn't really sure, but this is the only thing I could think of.

 

[rl.bhat]

What is the distance between the speaker?

 

[SilentBlade91]

this is all the information the problem gives

 

[rl.bhat]

Is there any diagram along with the problem?

 

[SilentBlade91]

The diagram is below..

 

[SilentBlade91]

Here it is it is inverted for some reason but still...

 

[rl.bhat]

If D is the distance between the plane of the speaker and th plane of the detector, and 2d is the distance between the speakers, and x is the distance of the point 4 from the axis, then
(1228.5)2 = D^2 -x^2...(1)
(1618.5)^2 = D^2 + x^2...(2)
No solve for x.
From the figure, it can be written that
x = nλ and n = 2. Now find λ.

 

[SilentBlade91]

Ummmm, I was very confused by that explanation. I am unsure what you are trying to do. And why is the distance between speakers 2d and why is that relevant? It didn't seem to be used anywhere. It seemed like pythagorean theorem was used in your explanation but something was subtracted for some reason and what were those (1) and (2) for?? I appreciate the help I was just utterly confused

 

[boogiepicker]

hey did you every figure out how to solve this problem? I am working on the same one and cannot figure it out. My professor is a bit of a dunce and he's of no use.