I heard that the car battery cannot supply current at a fast enough
rate
(because of chemical reaction neccesary)

You heard wrong. Current due to electron flow moves at the speed of
light.


You're right, Mark, but it is fair to say that a battery might not be
able to "supply current at a fast enough rate" in some instances. If
you have a large current draw that the alternator cannot keep up with,
and the battery has to make up the difference, you can get a
significant voltage drop due to the relatively high internal
resistance in the battery. (This is why even a "good" battery will
often drop down to as low as 9.6V while starting your car.)

That's correct. All power sources have an output Z. But that's quite
different from what he said. Especially in regard to his next comment.


for subwoofers and that a cap is
needed.

At what power ratings should one start to worry about this?

You should start to address whether or not a capacitor will help you if
your
headlights are dimming such that it's become an annoyance to you. When
that
happens, consider installing capacitors as close to the headlights as
possible. Oftentimes it won't be much more money to buy a high output
alternator or have yours modified by a shop. This is a much more
effective
tool to reduce dimming.

I would go even further and recommend upgrading the wiring to the
headlights before trying a capacitor.

I've demonstrated before (in a post to Eddie Runner about 6 months ago - the
math is there in a google search) that the headlight wiring makes no
difference.