In Fallout 4 there is no sound, despite the fact that all the sound work.
First thing to check for all drivers.
Make it better with the help of software Driver Restore. Software automatically checks all the necessary drivers and all updates itself.
Download: Driver Restore
If the drivers are installed go further.
The problem arises from the lack of drivers DirectX.
To solve necessary to install DirectX End-User Runtimes your OS windows.
Download: DirectX End-User Runtimes. After installing sound in Fallout 4 will operate as intended.