You can get dvi to pass sound through an adapter to hdmi.
Please refer to this forum
Quote k1114 " Dvi can actually output an hdmi signal which supports audio. But the dvi signal does not support audio. This works on both nvidia and amd cards. It depends if your card is capable. Any of the data pins can send a digital signal of any type (but keep in mind it needs to be dvi compliant), it's what creates the signal that is the issue. Different types of dvi is also irrelevant as this is just the number of pins (except for dvi-a since it needs to be digital).
Features specific to HDMI, such as remote-control, audio transport, xvYCC, and deep-color, are not usable in devices that only support DVI signalling. However, many devices can output HDMI over a DVI output (examples: ATI 3000-series and NVIDIA GTX 200-series video cards), and some multimedia displays accept HDMI (including audio) over a DVI input. Exact capabilities vary from product to product.
@OP make sure you have the proper drivers, Make sure your adapter is capable of transferring the audio and last we know from the above that your graphics card is capable of producing the sound and transferring it.