just signed up simply so i can put my two cents in, as this is the first and most specific google hit that comes up for this particular problem.
trying to turn off the shutter sound in instagram (specifically in instagram, as opposed to the stock camera, which most google hits lead to, despite typing "instagram" as the issue of the unavoidable shutter sound is more prevalent with 'regular' picture taking).
anyhow, just wanted to say that i had a fish around and found which file instagram uses for its shutter sound (something i couldn't find with google, hence sharing here).
i am using a Sprint Samsung Galaxy S2
i rooted the phone, then got the ES File Explorer app, then navigated to
/system/media/audio/ui
in there i renamed the file Shutter.ogg to Shutter.ogg.bak
went back to instagram (didn't reboot or anything) and the picture taking is blissfully silent now.
hope that helps someone else who is looking for the same information.
i don't have enough energy to take a real part in the "if you're trying to silence your camera you're automatically a pervert" discussion, but suffice it to say that i've been taking pictures for years, on all kinds of equipment, and not only is a huge percentage of photography (especially, if not specifically, candid photography) served best by discretion - as in being a passive observer silently interacting with a scene i am trying to solidify and preserve - but also no camera i have ever used makes such a loud noise as this like-it-or-leave-it noise that is now "required, due to issues of perverse picture taking." if it were required but there were a volume level, a way to make it quieter, i may not mind so much. but this sound which by design can no longer be turned off (depending on model and origin), is about as quiet as dropping my car keys on a wooden table. the requirement is an insult to respectful photography, to respecting the surroundings and the setting of what, where, who and how you are photographing.
furthermore, this backwards mode of thinking that has become so popular in increasingly less responsible societies whereby effect and result is dealt ever-increasing blows of legislation rather than cause and source is not only barbaric: it's just sad.