Verified answer

Sounds like a broken transmission mount or a bad u-joint. I'd check the mount first.

If you have already checked for dead bodies and debris under the car, maybe there are a few other things to check. Is this car rear-wheel-drive? If so, there could be something wrong with the driveshaft clunking around under there. If it is a front-wheel-drive, it may be some engine vibrations transferred because of worn motor mounts. In either case, it also could be exhaust pipes that have a loose piece that opens up and roars out under your seat in the middle of the car when you floor it. You can try revving it in neutral and see if it makes the same noise. If it does, you probably have exhaust problems. If it doesn't, you probably have drivetrain/motormount issues. Do you know anyone with an engine lift or a set of ramps? They would probably let you look under your car and help you find out what is going on.

It seems like your description points to the catalytic converter. This is a device used to reduce the toxicity of emissions from an internal combustion engine. It is located between your engine and the rear of the car. Likely, a clamp holding it, or possibly a bracket came lose while driving, or due to old age.

When you bring the vehicle in for inspection, ask the mechanic if you can take him/her on a drive so that they can experience the sound precisely as you do in order for them to diagnose it properly.

Assuming your car is rear wheel drive it sounds like the transmission mount is loose or broken. I'd get it fixed before something breaks from the knocking around.

If your car is rear wheel drive, it's probably your drive shaft or a dead cat. Hard to answer a question like that when you give no detailed information on your car. If you actually want to get free help instead of a mechanic telling you, "your out of magic cow ****." I would edit your question and and repost it...

Is the car rear wheel driver? Is it stick shift? If it's either of these, you could be looking at a drive train/transmission problem

sounds like it may be the transmission .......if its in the middle of the car under the seats

Go to a repair shop and get it fixed. The worst case is that its a Carbon monoxide leak. SEEK PROFESSIONAL HELP(not yahoo answers)

Could be your universal joint or a transmission problem.

get that checked out, it could be a loose part.