I've read his book and he talks about AC current frequencies of incredibly high magnitudes. How was this achieved? Surely he did not just spin his dynamo really, really fast.
Perhaps.. http://www.mentallandscape.com/Tesla1.htm It continues with a description of his later work including a spark gap LC transmitter. Basically this is a resonant circuit that is hit with an impulse to make it "ring" at the resonant frequency.
10 kHz is still in the acoustic domain (for sound). Why is this "such high frequency" according to you? When you say something is very large, or very small, you must tell us what physical quantity of the same kind you are comparing it with.