edit:

sorry !

false alarm ... just firefox nightly with no sound ...

never mind !
try to launch firefox on a terminal and see the log please, again without more precision i cannot help you
5 days later
if u insist ...

To play audio, you may need to install the required PulseAudio software.
firefox-nightly

(firefox:1594): Gtk-WARNING **: Locale not supported by C library.
        Using the fallback 'C' locale.
ATTENTION: default value of option force_s3tc_enable overridden by environment.
ATTENTION: default value of option force_s3tc_enable overridden by environment.

(/opt/firefox-51.0a1/plugin-container:1634): Gtk-WARNING **: Locale not supported by C library.
        Using the fallback 'C' locale.
Failed to create secure directory (/root/.config/pulse): Permission denied
5 days later
Sorry, i didn't saw your post.

Well, i am not understanding what happen on your system with this version of firefox, because pulseaudio is not a dependencie for firefox-nightly. i tried to install (with yaourt) it on my system and on fresh container to see trouble with dependencie. All those install work and pulseaudio was not installed.
So you can try to install pulseaudio software to see if the trouble persist, but honestly i don"t know how to solve your issue for the moment.

Anyway to install pulse, just do this 
sudo pacman -S pulseaudio
The soft try to make a directory on root directory and this is surprise me if you launch firefox with user privilegies.

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