Acceleration time of unloaded motor
$$M=J\alpha$$
$$\alpha=\frac{M}{J} = \frac{0.0946}{3.36*10^{-6}}\approx 28000\;rad/s^2 $$
$$dt=\frac{d\omega}{\alpha}= \frac{100*2\pi}{60*28000} \approx 0.4ms$$

You have to use the disk inertia in calc, as it is the major inertia of the system. While the sound frequency follows the square root of rotor frequency, I know because we did similar project at university.
After you calculate the real inertias you have to add also the rise time of your sytem.