really weird interference

My wife just bought an 06 Yukon Denali with a GM. factory AM-FM-XM-cassette-CD sound system. As we drove the car home from Cleveland to Detroit we listened to wonderful FM reception. Halfway home we changed to AM, only to find a Deep Buzzing sound in both the left and right channels. We switched to XM to find the same buzzing, but only in the right channel, the left was fine. I figured the radio had issues. We drove home listening to FM and the next morning I went out to the car, turned on the radio without the engine running, and everything worked great, AM, FM, and XM. I started te engine and the AM and FM sounded great but the XM had a background whining noise in the right channel only. I figured that the XM tuner had an output shielding problem into the main radio amplifier. A pain, but probably correctible!  I started driving the car with the AM band on and a loud deep clicking stared coming out of both the left and right  speakers, increasing in frequency as the wheels turned faster, At 10 mph the clicking turned into a deep buzz with no hint of a radio. I switched to XM and the same noise came out of the right speakers but not the left. Finally, I switched to FM and everything was perfectly clear. The unwanted noise was directly related to the RPMs of the wheels, not the RPMs of the engine. I am pretty sure the original whining noise in the right channel of the XM tuner is a shielding problem but how the turning of the wheels could knock out both channels of the AM radio and only the right channel of the XM radio is way beyond me. If anyone has any ideas I would really appreciate it. In all of my experience in diagnosing interference and reception, I have never seen, or heard of, the vehicle's drive train being an issue. I almost think this thing is haunted

does the car have aftermarket HID (high intensity discharge) systems?

you can tell if your lights are VERY bright, and they contain a slight hue or blue

If you do not care about the speed sensitive volume control, you may want to try and cut the speed sense wire from the back of the radio.  If it is a navigation unit, you will have trouble using the nav in a tunnel or a parking garage, other than that you should see no ill effects from cutting the wire.  Cut it far enough back to allow for reconnecting if need be.

Good call!  Another reply mentioned the speed sense and I completely forgot about the speed sensitive volume control. I am sure that is the source of my problem and I will confirm it tomorrow. Thanks a bunch to both of you. Hope I can help you someday