Disable sound alerts for new emails
See below how to change your email notification sound, or how to disable it. My android is 2.3.5, gmail is 2.3.6. 

You open the gmail app, menu > more > settings, tap in the account; in the very bottom there's an option "Labels to notify". In my case I have "Inbox", which I'm assuming is default; when you click on it, you have a few options:


"Email notifications" - notifies in the status bar
Ringtone - this is what you're looking for, you can set any ringtone or silent
Vibrate - well, it vibrates ;)