Help: '73 Mach1: Throbbing headlights?

Hi All. I have recently purchased a '73 Mach 1 Mustang, and the issue I am having is with the headlights - they turn on fine, and work fine on both hi and lo beams. When the car is either engine off with the lights on, or engine running and in idle, everything is normal.

BUT, when I step on the gas and accelerate the headlights "fluctuate" in their intensity (for example, they appear to go between 100% brightness and 50% brightness and back again about once every second.) It only seems to happen when accelerating; if I come to a stop at a red light, then no problem.

This is very noticable at night, and semi-embarassing when cruising around town! Any help shedding light on the matter much appreciated, as I have no idea what the problem could be or how to go about fixing it.

Sounds like an alternator/battery issue. Check to make sure your alternator is charging correctly and that your battery is good. Also check that your belts are not loose. If your alternator drive belt is loose than it may slip under acceleration, causing your battery to provide all the juice and making your bulbs dim. See if it isn't one of those things, as they are the most likely.