I can tentatively say that I have found a workaround after carefully reading bug 77010. Open gconf-editor, navigate to
Desktop->Gnome->Peripherals->Keyboard and set "bell_mode" to "off"
Why setting the keyboard bell to "off" would stop the indicator-applet from beeping on new emails is a question I cannot answer.
I can tentatively say that I have found a workaround after carefully reading bug 77010. Open gconf-editor, navigate to >Gnome- >Peripherals- >Keyboard and set "bell_mode" to "off"
Desktop-
Why setting the keyboard bell to "off" would stop the indicator-applet from beeping on new emails is a question I cannot answer.