What effect does a greater pressure difference have on wind speed?

A greater pressure difference results in an increase in wind speed due to the principles outlined in the Geostrophic Wind theory and the pressure gradient force. When there is a steep pressure gradient—meaning there is a significant difference in atmospheric pressure over a short distance—this creates a stronger pressure gradient force that pushes air from high-pressure areas toward low-pressure areas more forcefully.

Wind is essentially the movement of air caused by these pressure differences, and the stronger the gradient, the faster the air moves to equalize the pressure disparity. This is why meteorologists often look at the spacing of isobars (lines of constant pressure on weather maps); closely spaced isobars indicate a stronger pressure difference, which correlates with stronger winds.

The other options do not accurately reflect the relationship between pressure differences and wind speed. A decrease or no change in wind speed would contradict the fundamental behavior of wind driven by pressure gradients. Similarly, describing wind as erratic doesn't correlate with the established physics of wind behavior under varying pressure conditions.