I had a problem with speed wobble (or "shimmy" as it's also commonly known) a few weeks ago, on a sharp descent.
It's terrifying - I literally feared for my life and thought my front wheel must have come loose and was about to wobble off.
In hindsight, what actually caused the wobble was me shifting position - moving my hands from the hoods to the drops.
Braking only makes it worse, as does gripping the bars with a death-like hold!

I'm not much of a physicist, but understand it occurs when the bike reaches a certain frequency. The best way to stop it is to loosen the grip on the handlebars a little and rest your knee(s) on the top-tube. This alters the natural frequency causing the shimmy.

Despite actually knowing all this, when it happened to me, my mind went completely blank, I panicked and careered down the hill looking like I'd drunk the local tavern dry!

Some bikes are allegedly prone to wobble more than others (apparently dependent on the frame), although I'm not sure there's any substance to this arguement.
I'm now so paranoid about getting "the wobbles" again that I now grip the top tube between my knees as I descend, which seems to work as it hasn't happened again (and I've ridden the same descent several times since).
When doing sweeping turns, I also try and make sure one knee is resting on the tube.