Well, it's sinusoidal, innit?

The height of the water is, yes, but to figure out the speed of the tide you have to take the derivative of the sin curve, which happens to be the cosin curve. Where the sin curve crosses the x-axis (halfway between it's highs and lows) the cosin curve reaches it's maximums and minimums, meaning that the speed of the tide will be greatest in the middle.

I hope that was clear.