fluid dynamics - Why does the sound of my tea stirring go up in tone the faster I stir?

I've noticed that when stirring my tea, as I stir faster the tone generated by the stirring goes up. Why is that? Is it something to do with the Doppler Effect?

EDIT --------------------------

Thanks for the responses guys - Victor's and Carl's seem like good answers to the question. Unfortunately I realise I may have described the situation wrong - I think I may actually be hearing the pitch go up as I stir at a generally constant speed. It may have something to do with some accumulating increase in the velocity of the tea. But as that's my stupid mistake I'll tick Victor's response to this particular question.

Answer

I would go for this: Imagine the bottom of the cup as a saw. The noise or chattering of the spoon jumping on the sawteeth is higher the faster spoon moves. Those "sawteeth" on the cup bottom are very small, but the principle is the same. Therefore the faster stirring the higher pitch.