Beep sound when a new email arrives

We’ve set the Windows sound scheme to “No Sounds” as we are not to have any default sounds going off all day (I share the room with 5 other people). But now every time an email arrives, the computer still makes a beeping sound which is even more annoying. We cannot turn off the sound completely either as for some things we are still allowed to have sound alerts (in fact, it is required).
How can we get rid of the beep?

Disabling the sound scheme is not enough for Outlook as there is a separate option in Outlook to play a sound when a new email arrives. When you disable this option as well, the sound will go away.

Tools-> Options…-> button Email Options-> button Advanced Email Options…-> option: Play a sound

Further info
If Outlook is configured to play a sound when a new email arrives, then Windows will play the sound that is configured for “New Mail Notification” event in the Windows sound scheme. By default this is “Windows Notify.wav” or “Windows XP Notify.wav”.

If Outlook is configured to play a sound when a new email arrives but no sound is configured for the “New Mail Notification” event in the Windows sound scheme, then the sound for “Default Beep” is played. By default this is “Windows Ding.wav” or “Windows XP Ding.wav”.

If Outlook is configured to play a sound when a new email arrives but no sound is configured for the “New Mail Notification” or the “Default Beep” event in the Windows sound scheme, then the system speaker is used to provide feedback.

If Outlook is configured to play a sound and there is no sound card or the computer is otherwise configured to use the system speaker only, then the system speaker is used regardless which sound is configured to play in the Windows sound scheme.