audiobrowser-tabsfirefox
Firefox has an option to mute a tab. Particularly useful when a misbehaved website opened in a background tab suddenly starts playing a video with sound.
Is it possible to tell Firefox to open new tabs with muted sound by default, so that tabs will only play sound after I explicitly give permission to do so?
I would suggest avoiding the issue altogether by preventing video/music from automatically playing. Here are three things you can do (together or separately) to help prevent auto playing video/sound.
Install AdBlock Plus, which will block most advertisements including those that automatically start playing video/sound.
Go to about:config and set media.autoplay.enabled to false. This supposedly stops HTML5 media from autoplaying, though I couldn't find any references to it in the about:config entries on MozillaZine Knowledge Base.
Go to about:config and set plugins.click_to_play to true. As you can see, it stopped Youtube from auto-playing this annoying video. 
This action is controlled by a setting in about:config.
about:config in the URL window.media.block-autoplay-until-in-foreground. The default setting is false.True.
Best Answer
New tabs are typically given focus immediately when they are created, so this won't help in that case. Only new tabs opened in the background would be muted this way by default until you make one of them active.
Firefox 55.0.2 (64-bit) in Ubuntu 16.04:
about:config [I accept the risk!]
Search: media.block-autoplay-until-in-foreground [Double click the search result line to toggle the value between false and true.]
Reference: https://www.ghacks.net/2016/11/14/firefox-51-blocks-automatic-audio-playback-in-non-active-tabs/