Your wave anology sounds pretty good.
The thing about homeopathy is that we don't know all the mechanics about how it works. This bothers a lot of people, but we don't know how a lot of allopathic drugs (mainstream med) work, either. Except that it is in huge amts and has a worse track record for positive results and a much greater percentage of doing harm. It's frightening what they don't know about allopathic drugs. And they definately don't take the time to discuss the simtoms in such great detail as homeopaths do.
Homeopathy is older than allopathy. All the drugs listed in the Materia Medica are approved by the FDA because of the testing or "proving" process utilized by homeopaths. Basically, they take the drugs themselves and report the findings. It's a sort of reversal. If a drug (mineral, herb or compound) causes the symptoms of an illness, it is used to treat that illness.
But, you can't just take say salt and create or prevent the illness. Through a lot of testing they realized that sucussing the agent in pure water they were able to get to the essense and power of the remedy. Succussing happens when they place a small amt of the agent into water and shake it vigorously about 100 times (it's very specific, I don't recall if it's 40 or 100 times or different), then they take out 1 part and add it to 100 parts pure water and sucuss again. Every time a remedy is succussed in this manner it is counted. After hundres of sucussions you may get the final product. I believe some remedies are sucussed 1 million times. At this point even a molicule of the original agent is no longer traceable in the remedy. But, the property of the water is changed. This is the part that they're just discovering but don't have all the mechanics to. It doesn't change the fact that it works and works well.
I liken these facts to the unknown aspects of the universe. That is, unknown to science but known to mystics for thousands of years. The difference is that mystics know it because they feel it and scientists want to be able to quantify the mechanics. This isn't a problem as the more modern physics discovers, the more it looks like the wisdom of mystics.
One of the main things about homeopathy is the goal to do no harm. To trust the in the body's ability to heal itself. Homeopathy provides a little kick in that direction and the body does the rest. Some times this process may take a while, several months or repeat remedies. Sometimes the original remedy is wrong. But, they have basically the same chance of hitting on the right remedy after the first visit as an allopathic doc. Or better since they take more time to discuss all the aspects of the illness instead of just looking for clues and picking a drug.
Homeopathy is not a placebo, although we shouldn't discount the staggering power of the placebo effect. Homeopathy is medicine and it's practiced all over the world and in some places in far greater numbers than allopathy. And it's relatively inexpensive. And has virtually no side effects.
For further reading I'd suggest Health and Healing by Dr. Andrew Weil. More info: http://www.homeopathy.com/
but that's the college. This is my doc: http://www.naturopathyonline.com/
I can understand why someone would be skeptical of homeopathy, it looks fishy when taken in account from our western, allopathic, popularist-science mindset. But I believe it's more scientific than allopathy. Once you have the facts.