EAC causes the speaker on my computer (as opposed to the speakers plugged into the back of my PC) to beep on a fairly regular basis while ripping CDs. Why is this and is it something I need to be concerned about, i.e. does the beeping indicate some sort of error or problem?

It indicates extraction finish, you can turn it off by unticking "Beep after extraction finished" in General tab of EAC Options.