Dedicated Lines - Problem

I recently installed 2 dedicated lines (I thought!) but have noticed a loud pop through my speakers when the air conditioner and de-humidifier automatically switch on and off. My panel is made up of double breakers, each breaker controlling 2 lines. The air conditioner and the de-humidifier do not share a breaker with the stereo lines. Any suggestions what is causing the popping noise ... obviously, the 2 stereo lines are NOT dedicated.
Well, they could be dedicated and the noise in the line is merely backing all the way back to the panel and into the main power feed, and then going back down into the dedicated circuits. Did they put any sort of noise filter on the dedicated lines at the breaker? If not, this is what will happen.

(FYI: This is one reason why your stereo typically will sound better late at night, as all of your neighbors quit using their noisy appliances late at night, and the main power feed is quieter.)

But then again, imagine how bad it would be without dedicated lines at all.

Also, what gauge wire did they use for the dedicated circuits?
Kurt has made an excellent point. Check the gauge and an industrial noise filter might make sense.
P.S.: You might check on Audiogon here. Someone has reported on his set up specific to your problem some while back. Sadly I don't remember who it was.
Thanks for the suggestions. I will do a bit of research regarding the noise filter.
Kurt tank is right. The reason for the 'POP' could be that your panel is at max current draw. Add to that maybe some older motors that generate electrical noise. Another thing to think about when adding Dedicated lines is to 'balance' the load. What I mean by that is most homes have 2 phase power coming into the panel. Phase a and phase b. Now if the A/C - dehumidifier - refrigerator - toaster etc (follow me - high current devices especially electric motors) are on 1 phase along with your system there could be some very dramatic sags surges and spikes when those appliances turn on and off.

Did the 'popping' happen before the new circuits? If not you may want to have the breakers put on the other phase. Otherwise I might think about getting the motors and starting caps for the A/C and dehumidifier checked out.
The people above are on the right track,having your new dedicated line tied to the same phase leg in your breaker box as your dehumidifier,and AC if that is the problem.If it is a 240 AC,the problem will still leak through since a 240 AC uses both halves of the power line.A 120 volt AC only uses one side of the 240 volt line.Even your neighbors lines are tied to the same power lines as most most likely. They're just further away and less noticeable.Even a dedicated utility transformer will still have other peoples appliance noise coming through.A good power condition might help out as the last resort.Try switching outlets, or phase sides as suggested above.Its hard to describe without drawing a diagram.We hope you get cleared up though.
How old is your A/C system? Call your a/c company and make sure all electrical connections are tight all the way to the compressor. If it is an older a/c have them install a hard start kit. The hard start kit will help your a/c start better and easier. Loose connection can cause more noise because of arcing. When I installed my lines I made sure they were after the a/c in the panel to help keep noise away from my stereo. Some may say it does not matter where in the panel you are but I think it does.