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Because shutter speed and flash duration are not related until it gets out of sync. Typical shutter speeds range from anything up to 1/8000th of a second on a high end DSLR. A flash however has a duration from 1/40000th of a second up to 1/2000th or so depending on it's power output.
So assuming you're shooting below sync speed at 1/250th. The flash fires for a tiny duration while the entire sensor is exposed. If you open up the shutter you let more ambient light in but the flash still fires for the same tiny duration.
Above 1/250th the entire sensor is not exposed at once, meaning the rear curtain of the shutter starts closing before the front curtain has finished opening. It's literally dragging a slit across the frame. To illuminate the scene the flash has to fire multiple times. so at 1/500th the flash in high speed sync would have to fire twice, once to illuminate the scene when the first half of the sensor is exposing, and then again when the second half is exposing. Thus more power is drawn from the flash and you've effectively limited your max power output capability of the flash.
Because like Garbz said, the flash burst duration is very very shot, like 1/1000s at full power to maybe 1/10,000s at lower power levels. When you're able to use a faster shutter speed with a flash you're proportionally capturing more of the flash burst and less of the ambient light. It's a balance.Can someone explain to me why a higher sync flash tend to put more light from the flash into the picture versus dragging the shutter which allow more ambient light in the picture?
Pssst. Nikon lied. You can sync their electronic shutter cameras to a much faster x sync speed. Up to 1/8000. I think that's the limitation of the camera.