I searched the forums for Mini users experiencing odd noises from their netbooks. I muted my speakers but still could hear the faint, high pitched morse code-like buzzing from beneath the keyboard. Turning off the screen did not work as well. I think I finally isolated the problem after turning off WiFi and Bluetooth. I think the wifi card is creating some sort of feedback to the internal speakers. However, turning off the speakers did not prevent the feedback from occuring. Only when I turn off Wifi does the odd noise stop.
I will install an OS other than the stock Ubuntu to see if different drivers are better able to cut power to the speakers if indeed the noise is the result of feedback from the wireless card sending and receiving signals.
EDIT: After more testing. I dont think I can isolate the problem to just the wifi card. It seems that turning Bluetooth OFF but leaving Wifi ON, decreases the noise.
EDIT2: Turning off Bluetooth AND WiFi solves the noise problem.