How to high-speed photography with only 1/250 flash sync?

I have a Nikon D200, and a third-party external flash. I can get the flash off the camera with a sync cord so the light direction isn't a problem.

The problem is, I'm wanting to do high-speed photography, like water drops in mid air for example, but doesn't that require at least 1/640 to stop the motion?

Anyway, I can only use 1/250 as the fastest I can shoot, due to the flash sync and the "black bar" effect that shows up.

I've usually just been shooting at 1/250, f/11 or so, ISO 100. But i'm not getting the results I'm wanting.

Any tips/help on what I should do?

Remember that the flash unit will (or can) make the exposure.

That is… In near darkness (or, for example, in your kitchen sink with the lights off during an afternoon), even though your shutter speed is only a 1/250th, the flash fires at 1/1000th or 1/1500th second.

And it's the FLASH that makes (determines) the freezing-ness of the action.

Keep it dark and use the flash to make the exposure. If outside during daylight, use a neutral density filter to darken the view and set the flash to overcome the darkness (again… And to make the freeze-frame exposure).

The answer above is correct, but you DO have higher sync speeds available with the D200.

Go to your custom settings menu (the pencil icon) and go to menu e1: Flash Sync Speed Setting. Choose 1/250s (Auto FP). If you use M or S modes, you can set any shutter speed that you want and a Nikon flash (NOT the pop-up flash) like an SB900, SB800, SB600, it will sync. You would be able to go all the way up to 1/8000 with Auto FP High Speed Sync with a Nikon flash. I do not know if this works with a third party flash, but you may as well give it a try.