Period of Vibrational Modes

I am trying to understand more about the period of vibrational nodes. Currently, I am interested in the wavelength of the $\ce{Si-O}$ bond stretch in silica. I think this value is roughly $1000\mathrm{~cm^{-1}}$.


I am somewhat confused on how to find the period of vibrational modes. I am new to this subject. When I look up the frequency, like I said, I get units of $\mathrm{cm^{-1}}$, but I want units of $\mathrm{s^{-1}}$.


Any pointers on how I can get this value?


Is this the way to calculate it:


$$T = \frac{1}{\nu}$$


where


$$\nu = c \bar{\nu}$$


with $T$, $\nu$, and $\bar{\nu}$ being the period, frequency, and wavenumber respectively?


With this I get:


$$\begin{align}
T &= \frac{1}{c\bar{\nu}} \\
&= \frac{1}{(3 \times 10^{10}\mathrm{~cm~s^{-1}})(1000\mathrm{~cm^{-1}})} \\
&= 33.33\mathrm{~fs}
\end{align}$$


Also, as temperature increases, wouldn't the period decrease? But in the literature, I find that as temperature increases, the wavenumber decreases. Thus, the period increases. Why would the period increase? I would think at a higher temperature, bond stretching would occur more quickly. Is this not the case?


