You might try this mod DirectShow Filter _Codec_ Reset by Blade FireLight I have not had the issue personally so I cannot say for sure the solution. Some say install K-Lite, some say uninstall. I have seen posts relating this issue to audio codecs.
Do any other games give you audio issues? So even running it vanilla the music still fails? Try dropping audio quality and see if that changes anything. Fallout 3 runs fine and has none of the issues listed. The game used to run fine and it is 100% non-cracked, I bought it from steam and there's a receipt that proves it. Note: I have the Ultimate Edition, running Windows 7 64 bit. I don't know if anyone else has had this problem because I'm finding zero posts on the Internet about this issue. I completely deleted and then re-installed the game from steam and just tried it out with no mods and the stations didn't work right still. I used extra radio station mods so the tracks didn't repeat to much, but those stations stopped working also. New Vegas give the news or introduce the song that's about to play, but when its supposed to come on, there's no sound, the in-game ambient soundtrack just plays over the silent radio stations, like Mojave music radio.
To top it off my game crashes EVERY time I exit it, no matter what. I don't know what happened, or what I did wrong, but all of the radio stations don't play music and some dialog from NPCs are inaudible.