Interpolation by factor of 2
When you upsample by a factor of two by inserting a zero between each sample you create an alias of your signal centered at the new Nyquist frequency (half the new sample rate).  You get rid of the alias by low-pass filtering.

The specifications of the filter that you need depend on your signal.  Say that your signal has one-sided bandwidth $B$ (by one-sided I mean that we are only talking about the positive frequencies, not the negative ones).  $B$ must have been less than the Nyquist frequency of the old sample rate, $f_{sOld}$, to avoid aliasing.



Once you upsample the alias appears.



Hopefully these pictures will help to gain an intuitive grasp of how to characterize the required low-pass filter.  The passband must be flat from 0 Hz to $B$ Hz, and it must cutoff at $\frac{f_{sNew}}{2} - B = f_{sOld} - B$.  The amount of attenuation that is required in the cutoff region depends on your application.  Usually 50 dB is more than sufficient.