I know this seems silly. Obviously I could mute my computer, or turn the speakers off. But it seems like surely there should be a way that I can keep all of my normal computer sounds without having to hear this one sound (no, it doesn't really bother me; mostly my wife just wants me to turn it off because she finds it annoying).
I tried right-clicking on the volume icon in the notification area and went through all of the sounds in the list, thinking I could find the one offending noise and just turn it off. But none of them seem to correspond to the sound that plays when my wireless adapter randomly disconnects and reconnects to the wireless network.