Is it possible to start a process in such a way that it cannot access a particular file? For example, I would like to mute all sounds in Firefox. I thought a way to do it would be to deny Firefox access to /dev/dsp. Can this be done?

I guess a rough way would be to chroot the process. Instead of bootstrapping a new os in it, I could just symbolically link a bunch of stuff. I'm sure there's a better way though.