It could be a few things.....
1. Remote Turn on to your amp is hooked up to an accessory wire. When you turn on the key the amp is on, with no signal input sometimes the amp will pulse the sub like that. Boils down to inproper installation if you were not told about this when it was installed or a faulty head unit but not likely.
2. Bad ground....I have never experienced a bad ground pulsing a sub, but I dont know what amp, deck, or sub your running so it's a possibility.
3. The installer used cheap RCA cables and ran them next to the power wire. This is happens all too often. Cheap RCA will pick up a signal from the power cable. The audioable noise you hear usually goes with the rpm's of the engine but then again I dont know what equipment your running so I cant say for certain.
4. My first guess is this one......The installer might have run the RCA's under the carpet and somewhere in the RCA line there is a short that is grounding out. For instance: if you run RCA cables in a vehicle and barely knick the RCA cable with a screw that holds down a panel, once the screw is grounded over time the RCA cable can develop an exposed wire where the screw is partially through it and become grounded out causing noise in the sub.
5. I would also check is the battery, it's not likely but as a car audio store owner I have seen odder things go wrong. Again not knowing the equipment you might have too much draw from the battery causing the amp to "clip" or "Low Volt". Low volting an amp often time causes bizzare and unusual noises.
6. Lastly, you might have a blown sub or a sub on the way out. I have seen this before....A sub that is near the end of it's life will act bizzare and do funny things when the unburnt portions of the voice coil make a good contact and the sub comes back to life.
Just a few things to look into on your own, I would think the place who installed it would warranty their labor and look at it free of charge. I know I would if we installed it ay my shop. Try taking it back to who installed it and see what they some up with. If the noise is driving you crazy unplug the sub.
Good Luck,
Steve