HAHAHAHA!!! This is the best thread I've read in weeks! 007mm boy is the best thing since Dude16.Man, Freud would have a feild-day with this.
Firstly, you *could* theoretically run a subwoofer from a deck. My pioneer P430 has a built-in option to run a sub out the rear-channels, complete with low-pass filters.
But that's a special case.
First of all; Here's some information for the little children:
POWER-HANDLING; This is *THE* most abused method of rating ever used. There are two main types; Max. Power handing, and RMS power-handling. Max handling refers to how much power the unit can take before it fails. RMS power refers to how much power the unit can take, with a pink-noise signal, for 8 continuous hours without failiure.
But there's even more to it than that. When you describe "Power Handling" and "Failiure" you aren't specifying what is failing. There are 2 main types; You have thermal failiure, when the voice coil actually melts, or Mechanical failiure, when the voice coil gets pounded apart, or the surround tears free, or the spider gets ripped apart.
Most cheapie-brands rate their power-handling as THERMAL failiure, to wit, the power at which the voice coil vaporizes. The speaker will start distorting and bottoming out WAY before it reaches thermal peak. This makes the subs look better on paper, but really, who cares how hot the sub can get before vaporizing, right?
More expensive (and reputable) brands rate based on a combination of mechanical and thermal properties of the unit. They take the engineered X-max (excursion) of the woofer and combine it with the heat-dissipating properties of the coil(s). The end result is that you may get a lower rating. But that rating will be accurate, and the output at that power will be consistant. You can make cheaper woofers distort when you throw less power than even the RMS rating at them. Or, you can throw more power at a better woofer than it is rated at; I had a Kicker c-12 that would not distort even a *little bit* before it'd start bottoming out. And that was when I was throwing close to 800w @ 2ohm into it. The woofer was rated at 500w max.
But on top of that is the amp behind it. There are things to consider, like "Cone-control," THD(%), and power-spiking.
First of all, mis-matching components is risky business. In general, you want a higher-powered amp than speakers. But when you match, go by RMS, not MAX power. Going the other way creates HUGE problems.
Firstly, a lower-rated amp doesn't have any measure of power throttling other than a thermal breaker. This means that if the amp heats up too much, it cuts out. An amplifier circuit is a very simple design. You can't throw too much into it without a) going digital or b)creating distortion/noise.
Basically, the amp will keep putting out power until something stops. If you shorted out the outputs, for example, the thing would fry before the thermals cut out, due to the massive current surge running through it. I=V*R, people. Putting a monster 2-ohm 18" woofer on a deck *WILL* melt it in a matter of moments.
There are 2 things that take up power in a speaker. First, there's the resistance of the coil itself. This is usually about 4ohms in a car-audio system, but can be as low as 2ohms or 1oh. Next, you have the amount of work that the power-source (amp) has to do to actually MOVE the cone. This will make the power that's being drawn go through the roof on a larger speaker. Remember, that wattage is just a measure of work done. And work can either mean "Air moved." or "Heat generated."
Now, based on design, an amplifier circuit will continue to dump as much power as the device it's driving asks for. The limiting factors are a) Thermal shut-down, b) Mathematical limit (based on power source) c) Amplifier gain, and d) source voltage.
You'll NEVER reach a the mathematical limit on the amplifier. Well, not for longer than a couple of nanoseconds, anyway. We've talked about thermal shutdown and vaporizing 
.
Your gain describes the amplitude at which you are amplifying the incoming signal. This is based on the specs of the control system being used, potentiometer size etc. Basically it's used to balance the incoming signal to the amplifier's outgoing power output, so that you don't over-stress the amp.
At a certain point of amplification, you start getting signal loss, simply due to the physical limits of the components to amplify the signal. This results in "clipping" which means the peaks of the sound wave ar chopped and flattened. Not only does this make it sound terrible, but it also excerts HORRIBLE stress on the woofer, from a thermal, and mechanical standpoint.
Most waves are nice and sloped. At the top of the peak, it levels off gently, and starts to fall. Remember that the speaker tries to follow this line EXACTLY. In a regular sinewave, the slop starts off gradual, and increases as it approaches vertical, then decreases and starts heading down. Imagine the stress on the amplifier and the speaker if half-way up the slope, when the woofer is at it's maximum velocity, it's suddenly told to STOP dead. The woofer is riding on an electromagnet, and it is the AMP that has to work to make it move, and stop.
You get massive current spikes as the amp tries to stop the cone (with varying degrees of success), which can damage internal components on the amplifier, and cause thermal stress (or mechanical stress) on the speaker.
Basically it's a bad thing.
So um, yeah. 007 sucks ass. 
