How to keep my muted mac from automatically un-muting itself

I specifically mute my laptop because I am going to be somewhere quiet (eg. classroom). While I'm using my laptop, I sometimes bring up a video in another tab and the laptop will for some reason un-mute itself without permission to play the audio of the video.

I feel like my physically muting the computer should override the computer's automatic responses, but that is not the case. Is there someway to change it? So when I push mute, I mean STAY MUTED until I push unmute?

Thanks for any help on this matter