Find the frequency of a wave whose time period is 0.001 sec.
A wave that has a period of 0.001 seconds has a period of 0.001 seconds per cycle. If you have 0.001 seconds per cycle, you have one cycle per 0.001 seconds. And one cycle per 1/1000 seconds is 1 x 1000 / 1 cycles per second, which is 1000 cycles per second.
As regards waves, frequency and period are reciprocals. By definition, 1/frequency equals period, and 1/period equals frequency.