Might not be relevant but if it's an older computer graphics card as the source there's often a connection on the card that you link to your MB/Sound card SPDIF header to get the sound on to the DVI output.
As you can see , for the first channel , HDMI and DVI are pin for pin compatible and there is no line for sound on either connection. All any DVI to HDMI adaptor does is rout the relevant pin numbers on one connection to the relevant pin number on the other connection.
HDMI inserts audio into the blanking period intervals between video frames. This is done in the HDMI chipset within the Devices itself.
DVI does not normally carry audio , but its got nothing to do with adaptors or cables , its the source electronics that decide that.
Some computer graphics cards have options to attach an spdif connection and the electronics then insert the audio into the signal so that its playable on a HDMI receiving device or "sink".
So , any DVI to HDMI adaptor should carry audio if the DVI source has some way of integrating the audio into the signal.