When You unplug your powered speakers & har a hum it is normal. This is noise from an ungrounded line. If you put your finger on the very end it will get louder. If you put your finger on the all 3 metal strips or just the 1 closest to the plastic of the plug, noise will cease. As for a normal soundwave it would look ragged & peaked as opposed to a standard sine-wave. It's level could be any where from 1 0r 2 mV[millivolts] up to 1 or 2 Volt depending on the board...
For this you may want to go to Control Panel > Sound , Dbl Click & make sure your deviceis enabled and there is a meter with a bar jumping up and down like the music would make it do.
If you have a Control Panel or Audio Mgr for the onboard sound or the sound board itself, open it and go thru to make sure nothing is amiss there.
Also be sure to check the obvious, ex.: headphones not plugged so that sound to speakers is cut off.....