I need a melody that is played when the new research is done
Heh, what Tristan is asking is which civ are you playing? The tune played when you get an advance is your nation's own "anthem", so it's different for each nation. If you're playing as the English, it's a snippet of Elgar's "Pomp And Circumstance", or if you are playing as the Americans it is a half-bar of "The Battle Hymn Of The Republic".
These are also the signature tunes played when you meet an opponent's ruler. Thus if you're playing as England, and you meet the Americans, you hear the Battle Hymn. These sounds are stored in your CIV directory as separate files, not embedded into the civ.exe itself, so you already have them.
Navigate your computer's file system to the CIV directory and look for .WAV files. There are 14 of them, one for each civ, plus a few more for other events in the game, like winning or losing battles, starting the game, winning or losing the game, special sounds for cannon attacks and nuclear weapons, et cetera.
What you are looking for are the "anthems", which are:
alex.wav = Alexander of the Greeks
ceas.wav = Caesar of the Romans
eliz.wav = Elizabeth I of the English
fred.wav = Frederick of the Germans
gand.wav = Gandhi of the Indians
geng.wav = Genghis of the Mongols
hama.wav = Hammurabi of the Babylonians
linc.wav = Abraham Lincoln of the Americans
mao.wav = Mao Tse Tung of the Chinese
mont.wav = Montezuma of the Aztecs
napo.wav = Napolean of the French
rams.wav = Rameses of the Egyptians
shak.wav = Shaka of the Zulus
stal.wav = Stalin of the Russians
Even if you customize your tribe and ruler's name at the start of a new game, you are still playing "under the colors" of one of the standard civs, which is indicated in the input area where you type in your own tribe's name. If it says "Americans" before you type in "Teletubbies", then through that whole game you will hear "Battle Hymn Of The Republic" every time you achieve a scientific advance.