There are two broad categories of display modes: CEA (TV style resolutions) and DMT (monitor style resolutions). The former is driven with HDMI signalling which supports audio, the latter with DVI signalling which doesn’t.

That being said, you can drive DMT modes with HDMI signalling and still have audio, but according to the spec, they don’t have to support this, and may just report unsupported mode and give no picture. That is why this setting has to be enabled manually in /boot/config.txt (by default, sound will only work in CEA modes):

hdmi_drive=1    # default, DVI mode
# hdmi_drive=2  # forces HDMI mode rather than DVI

Other settings may also need to be uncommented for the Pi to force an HDMI output when the monitor isn’t being detected as HDMI-ready, like:

hdmi_force_hotplug=1

Having the option that gives video and no audio as the default one is safer than an option that may give no video. Many computer monitors don’t support audio, so this shouldn’t be an issue. However, there was a time when the EU imposed import tariffs on TVs, specifically 16

Valid modes can be found by generating a edid.dat file from which one can also find the preferred monitor resolution (included in config.txt as hdmi_mode=<num>):

tvservice -d edid.dat`
edidparser edid.dat

If you try to run tvservice and it throws an error about not being supported when using the vc4-kms-v3d driver, run:

run sudo raspi-config

then go to Advanced Options > GL Driver > Legacy, and try again.

If the display is flickering, then this option in config.txt will generate a stronger video signal:

config_hdmi_boost=4   # default is normally 2 or 5

For optimal performance, start with the lowest value and work up incrementally, rebooting after each change, to identify the lowest reliable setting. While the value can be increased up to 11, this is only recommended if you’re using very long cables and experiencing persistent issues.