This will depend on the sound files with the particular aircraft & how they're configured. Open the Sound folder of the Cobra to check. If it contains more than one file (WAV) it has its own sound. If there's just one file (Sound.cfg) in there it will be aliased* to use the sound of another aircraft. Many CFS2 helicopters will be aliased to the FS2000 default Bell206B. You can download the special Helicopter Base file from CFS2 Misc which is configured so these will work properly in CFS2. You could also look round for a 3rd party sound package for the Cobra. I suspect most helicopter sound packages will be intended for FS & use default sound files not included with CFS2.

*PS. My Aliasing article explains the basics. http://www.simviation.com/lair/aliasing1.htm