[Rwillia4]

Sound more like they are sharing a common power wire. When the bass hits it sucks up all the available power that can get thru the wire that is causing a drop in voltage that reaches the gauge. Typical stereos have two power wires to hookup: main power and switched power.

The main power wire should go directly to the battery (an always on power source, not to a post that splits the power to many components because it will suck the power available to these components). The main power wire also supplies the radio with a power source when the key is in the off position allowing the radio to retain its memory of settings (yes, your radio will always use some of your battery power so if you are going to store your vehicle for long period take note).

The switched powerwire doesn't typically draw a lot of power its main purpose is to supply voltage only when the key is turned on a good source for this is usually a elec fuel pump (some will say this could possibly blow the pump fuse then the car doesn't work, however the fuel pump draw is continuous and typically not that high..pack a spare fuse in your tool bag).
Ground wire. If you rev your engine and hear a whine thru the speakers that goes up and down with the RPM you picked a bad ground location.
Induction thru the wires, not very likely you're talking about less than 1/2 amp thru any one line to a speaker.

What do you need to do? Change your power source for the radio to the battery, it is usually a yellow wire.