When new mail arrives, you can Thunderbird do several things to let you know. First, is to show an alert. The second is the animate the dock icon. The third is to play a certain sound. However, to set up one of these options, you must go to the program preferences: (Mac) Thunderbird > Preferences, (Windows) Tools > Options.
On the General tab, you can setup your new messages alerts under the heading “When New Messages Arrive…”. Here is what each options does:
Show an Alert – a message that says, “You have new messages”. It will force you to click OK for the notification to go away.
Animate the dock icon – this bounces the dock icon (on the Mac) until you click on the program. This option can be pretty annoying, but like the Show Alert, it can be good if you need to know right away when new messages arrive.
Play a sound – this does just that; it plays a sound. You can have it play any system sound you want, or you can have it play any .wav you have on your hard drive. To set this up, follow this tutorial.