Hello everyone!
First of all, thanks for all your help!
After I posted this HMDI sound output issue, I've searched all over the internet for answer and I eventually I found an easy fix by accident.
To have sound passing through my HDMI connection directly from my Mac Mini to my Monitor (using only the HDMI cable), in this case a SAMSUNG T27A550, I did the following:
1 - Before your turn on your Mac or Monitor, make sure no analog Audio cable (3.5mm) is connected to your Mac Mini's output, neither to your Monitor analog Audio Input port.
2 - Turn on both the Mac Mini and your Monitor.
3 - In your MAC go to System Preferences/Sound/ --- In both the SOUND EFFECT and OUTPUT tabs designate your HDMI device as the OUTPUT source. In my case, my Monitor's model was the only choice available besides the INTERNAL SPEAKER (Built In Audio).
4 - In your Monitor's remote control select SOURCE and scroll to the HDMI port (which will be highlighted) and press TOOLS (also on the remote control).
5- Select EDIT NAME.
6- Choose PC and hit Enter in the remote control.
Play any audio and turn up the volume of your Monitor using its remote control. You should be able to listen to audio via your Monitor's speakers by this step.
Bear in mind you won't have the usual Mac keyboard volume control. These will be disabled. You will have to control the volume using your Monitor volume control.
If you want to have the Mac Mini's keyboard volume control, to the following:
1 - Connect an analog audio cable to both your Mac Mini's output and your Monitor Audio Input.
2 - Turn on both the Mac Mini and your Monitor.
3 - In your MAC go to System Preferences/Sound/ --- In both the SOUND EFFECT and OUTPUT tabs designate your INTERNAL SPEAKER (Built In Audio). OBS: If you try to choose your HDMI option, the software won't allow it for some reason.
4 - In your Monitor's remote control select SOURCE and scroll to the HDMI port (which will be highlighted) and press TOOLS (also on the remote control).
5- Select EDIT NAME.
6 - Choose DVI PC and hit Enter in the remote control.
You should be able to listen to sound by this step from your Monitor's speakers. To control the volume, you can use both your Mac keyboard volume control and your Monitor Volume knob in the control remote.
It is an easy fix, but it was quite tricky to figure it out.
Anyway, I hope it helps anyone with the same issue.
Cheers!!!
