AMC 12 2003b Problem 23

The number of $x$-intercepts on the graph of $y=\sin(1/x)$ in the interval $(0.0001,0.001)$ is closest to

$\mathrm{(A)}\ 2900 \mathrm{(B)}\ 3000 \mathrm{(C)}\ 3100 \mathrm{(D)}\ 3200 \mathrm{(E)}\ 3300$