- #1

Saraphim

- 47

- 0

## Homework Statement

Two speakers at (x,y,z)=-L,0,0 and (x,y,z)=(0,-L,0)

Find the amplitude at all positions in the plane x=y

## Homework Equations

The waves are given by:

[tex]\tilde{f}_x(\overline{r},t)=\frac{A}{r_x} e^{i(kr_x-\omega t)}[/tex]

[tex]\tilde{f}_y(\overline{r},t)=\frac{A}{r_y} e^{i(kr_y-\omega t+\delta)}[/tex]

And the amplitude A is real.

## The Attempt at a Solution

I'm unsure how to proceed here, at least with finding the amplitude in the plane itself. I'm thinking that the amplitude for all points must be given by the real part of

[tex]\tilde{f}(\overline{r},t)=\tilde{f}_x+\tilde{f}_y=Ae^{-i \omega t}\left( \frac{1}{r_x} e^{i kr_x} + \frac{1}{r_y} e^{i(kr_y+\delta)}\right)[/tex]

But how do I go from here and to only the x=y plane? Do I just set [tex]r_x=r_y[/tex]? How does this carry any information about z? I think I just need a nudge in the right direction.