External monitor on HDMI but no sound

Solution 1:

From what I can tell from reading the Specifications Page, there are no speakers built into this particular monitor. There are however, two different audio outputs: HDMI 1.3 and 3.5mm headphone/speaker jack

The easiest way to test this out is just get a cheap set of speakers or a headset with the 3.5mm jack and plug them in. If it works, you know all is well with your setup - you just need speakers.

Solution 2:

If the screen is connected and switched on, you can select the speakers of your HDMI screen in System Preferences > Sound > Output.

Or if you have the audio volume button in your menubar, you could select it through OPTION + click on audio button. Then select the output device.