If you are not connecting directly to the TV, you may try that. I had an HDMI switcher and I was only getting video. I plugged the cable directly to the TV and I got both sound and video. Or it could be a faulty cord.
But the Nexus 10 itself should give both sound and video. No special app should be necessary. If you can play it on the Nexus, you should be able to play it over HDMI. (Unless its HBO Go, I read that they disabled playback over HDMI)
I found several threads from different android devices with HDMI out having this issue. Sometimes, it just seemed that some combinations of devices and TVs just didn't work, Sometimes it was just having a switch, AV receiver, or something else between the device and the TV. Sometimes it was just a bad cable.