We can edit browser’s internal sounds’ settings (”find in page” sound) but there is no way to turn off Flash sounds in Firefox via its settings or extensions. It doesn’t mean, however, that it is not possible.

Get rid of Flash sounds

Download FlashMute for Windows

Music, clicking noises and audio ads turning on whilst listening to the music or interrupting the night silence are the most annoying thing. Unfortunately, there is no plugin to turn off sound in Firefox.
However, there is a way to get rid of all the Flash sounds on Windows platform. The solution is FlashMute, a small application that resides in the systray.

After installing it, you will be able to easily mute/unmute sounds from any kind of Flash movie or the whole browser with Ctrl-Alt-M keyboard shortcut.

Unfortunately, this application only works in Windows OS.

Edit “find in page” sound settings

I personally use the Find option all the time. Pressing Ctrl-F (Cmd-F on Mac) or forward slash (/) enables you to find desired phrases in the opened website.

Although this is extremaly useful, the sound played when the typed phrase is not in the website may be a bit annoying. And if you watch the website, not the keyboard, while typing, you do not really need it.
It can be easily changed or turned off via about:config page.

Type about:config in the address bar, and enter accessibility.typeaheadfind.enablesound in the filter.
Double click on the entry and the value will change to false. To let you know that the value is different from the default on, the line will be displayed in bold.

If you just want to change the default sound to a less annoying one, you have to edit accessibility.typeaheadfind.soundURL entry on about:config page. Double click on the entry and in the new window enter the path of the desired audio file. It needs to be in Firefox format, e.g. file:///C:/sounds/beep.wav

For the changes to take effect you need to restart Firefox.