Had this problem with Skyrim when it came out. This MIGHT fix it - Right click the speaker icon in the bottom right on Windows, and press "Playback devices" then highlight your speakers (will probably be one with a green tick) then click "properties" in the bottom right. Head to the advanced tab and change the "default format" to 16bit 48000 Hz (DVD Quality) or any of the other ones See if that works!
Der er også en del der skriver om DX problemer, kan måske afhjælpes på denne måde?
Hey mate, don't know how you got on but another thing I read was to reinstall directx. Theres a directx folder within your "steamapps/fallout4" and you should be able to run direct x there to do a reinstall.