Wave Interference - Phase Difference

[planauts]

Homework Statement

I have another Wave Interference problem that I am having trouble with.

[PLAIN]http://img199.imageshack.us/img199/6104/questionsv.png

Homework Equations

[PLAIN]http://img151.imageshack.us/img151/3535/hintg.jpg

The Attempt at a Solution

f = 90.0 MHz
λ = (3E8)/(90E6) = 3.33 m

Let x, y, r represent the following
[PLAIN]http://img852.imageshack.us/img852/5836/questionso.png

Eq. 1
(x) - (r-x) = λ

Eq. 2
(x+y)-(r-(x+y)) = 0.5λ
2x + 2y - r = 0.5λ


Somehow I have to find the distance y. I am not exactly sure how I would go about solving this because I have 2 sets of equations (one with 2 variables and other with 3 variables).

Thanks,

 

[olivermsun]

Somehow I have to find the distance y. I am not exactly sure how I would go about solving this because I have 2 sets of equations (one with 2 variables and other with 3 variables).

Okay, let's try and tweak your equations slightly (while trying to keep your variables the same):

Eq. 1
(x) - (r-x) = nλ
2x - r = nλ

The original path difference is any integer multiple of λ (doesn't matter what n is) for constructive interference.

Eq. 2
(x+y)-(r-(x+y)) = (m + 0.5)λ
2x + 2y - r = (m + 0.5)λ

The path difference at the new position is some (possibly different) integer multiple mλ plus the half wavelength for destructive interference.

Now subtract Eq. 1 from Eq. 2 to eliminate 2x - r:

2y = (m-n + 0.5)λ

The problem asks for the minimum y, which just happens when m = n, and you can do the rest...

 

[planauts]

Sorry for the VERY late reply.
I got y = λ/4 = 0.8375 m

And that matches with my textbook's answer key.
Thank you so much for your help.

So basically what I should have done is subtracted the second equation from the first. That would have allowed me to eliminate the nasty R and X. Thanks again!