I have noticed that when I use Pale Moon, Duolingo cannot detect that I have a microphone, and the Microphone settings do not appear on the Settings page.
In contrast, I used Chromium, and lo and behold the microphone settings appeared.
I am not sure if this is a bug or if I need to adjust a browser pref, or what.
To test this yourself, I believe you will have to create an account at Duolingo. (It's free.)
PM 27.8.2 (64-bit)
UPDATE: Also tried it with Seamonkey 2.49.2 and got no microphone, and with Brave 0.22.13 and did get the microphone.