If you hear sound in Firefox then you can click the Volume icon in the system tray area on the Windows Task bar and mute the Firefox application.

See What to do if Firefox won't play any sounds

Hi,

I would really like to have a MUTE button for my browser. I have tried several addons, but somehow they do not mute every site or mute the entire soundcard.

When I play music, I do not want to get the website sound together with mine music.

Hoe can I request such a feature for the Firefox browser (and not as an add-on)?

You can submit feedback here: http://input.mozilla.com/en-US/feedback

You can't do that in Firefox.
Your only option is to use extension like Flash Block or Adblock Plus to prevent that content from loading.

• Adblock Plus: https://addons.mozilla.org/firefox/addon/adblock-plus/

You need to subscribe to a Filter list (e.g. the EasyList).

• http://adblockplus.org/en/subscriptions
• http://adblockplus.org/en/getting_started

• Flash Block: https://addons.mozilla.org/firefox/addon/flashblock/

• Stop Autoplay: https://addons.mozilla.org/firefox/addon/stop-autoplay/

A newly created extension (Muter) provides such feature. You can have a try: https://addons.mozilla.org/en-US/firefox/addon/muter/