I can't hear any audio while playing Youtube videos nor anything else from Firefox but I can hear the audio from my monitor's speakers.
My output device in sound options is set to my headphones and re-switching or re-plugging the headphones does not help.
I could not find any option to switch the Youtube audio from speakers to headphones.
Open terminal (ctrl+alt+T), then from terminl prompt open Alsamixer
Hit [F5] to display all sound channels.
Pan across to Headphone and check it is not Muted "MM"
If it is, hit M to unmute.
If in doubt, set all output channel sliders to high volume.
Then exit.