First of all, lots of monitors do not have speakers. Using an HDMI cable with a monitor that doesn't have the ability to produce sounds will not give you sound.
Also, monitors that do have speakers tend to have crappy sound quality. OK, maybe I'm biased, with my $200 speakers I wouldn't expect much from the speakers on a $200 monitor.
What I'd recommend is using a DVI or HDMI cable for video, between the graphics card and the monitor; then another cable for sound, between the motherboard's sound outputs and some proper speakers. Even cheap speakers should do better than what you get with the monitors.