Energy of interfering standing wave

[jagedlion]

Okay, I know that I should know this, but its just been a while so here it is:

I have a few emitters at 2.5 GHz at different points on the edge of a sphere of water. I want to find the RMS energy transmitted into the water in the sphere. Ideally by moving emitters/adding a phase delay, I can create an interference pattern that puts a hot spot arbitrarily where I want it.

I'm not worried about finding a rigorous answer, I'm just fine with matlabing it so long as I know what it is that I really need to do.

What I was thinking:
Represent the signal from the source as a sin wave. (Already with the appropriate phase delay to put a peak at the 'hot spot') Add the amplitude of the wave from each source. Square it and integrate it over one period. Divide by frequency and take the root to get RMS power.

Where I run into problems:
I cannot for the life of me remember how to get how the wave attenuates as it goes through the water.

So, 1. What have I already done wrong, and 2. Can someone please help me the rest of the way?

Thanks a lot,
Jon

 

[aim1732]

Point sized sources?

 

[jagedlion]

Yeah, let's keep things nice and full of assumptions.

It's more of a thought exercise, I'm not really planning on implementing.

Plus a 1/4 wavelength antenna for 2.5Ghz in a water medium (assume antenna in the sphere, rather than air) is what... like a quarter of a centimeter? I figure that's close enough. Considering that the antenna is really only broadcasting into a limited arc I was guessing that we could ignore the fact that the antenna probably isn't perfectly omnidirectional without being too naive.I would assume amplitude is basically a square drop (P=P0 / (4piR^2)) as you go deeper due to the wave spreading out over the surface area of the arc, and probably an exponential drop due to attenuation P=P0*e^-ar? Something like that?

So in total is would be P=P0*e^-ar/(4piR²) ?

Do I need to worry about the water changing the phase of the wave?

I'm just reasoning this out, so please let me know if this is roughly correct. If it is, where do I find the value of a?P.S. Also, I just realized I was being stupid, I didn't mean standing waves as in the title, the entire point of the design is that the position of the probes can be imperfect and corrected through phase delays. The rest of it is what I meant though.

I hope you are having a nice weekend.