Many sub-woofers are powered direct from the battery (if they are high power), so even with the sound system "off" they will still hum or thump.
I have had this problem also (on several cars) especially with non-factory installed amps.
It has to do with the class of amp, and the need for LOTS of current on amplifying bass of any loudness when at VERY low frequencies.
A gross oversimplification of this is that many of the amps "modulate" the power supply output to "drive" the amp transistors.
Remember all you technical folks, I am oversimplifying the explanation here.
The current draw is high, but "on and off" with the freq of the sound, so at any given second, it may average low enuf to not fry wiring.
Because of that need and others, they usually connect direct, and they almost NEVER have any effective radio frequency filtering.
So what can happen is RF getting into the leads of the amp pass thru and become unwanted audio, or RF gets into the speaker wiring and "backfeeds" the amp, and you get rectification noise.
If lowering the TX power reduces or eliminates the "interference", that is a good sign that you could filter or isolate the RF getting in.
You might clear it up by doing any or all of the usual RF interference techniques.
Even just twisting the power lead to the amp or re-routing the leads away from the antenna or radio may work.
Sometimes just using duct tape to hold leads (power in or speaker out) tightly against the car sheetmetal parts will fix it.
Just think of all that wiring being like antennas everywhere, and try to make them be poor antennas.
Even clamp on ferrites at the amp may be worth trying.
Just depends on how bad the trouble is.
I had one Explorer with a really high end system that I had installed, with a 1 Kw subwoofer that I never could get the hum out of, so I just hooked up a remote relay to disconnect the power when transmitting.
