Macbook air internal mic not working

https://everymac.com/systems/apple/macbook_pro/macbook-pro-retina-display-faq/

Hard to say without knowing exactly what Mac you have and what specs, but most likely reason would be your system doesn't meet the requirements (From Apple support site) - To install Mavericks, you need one of these Macs:

• iMac (Mid-2007 or later)
• MacBook (13-inch Aluminum, Late 2008), (13-inch, Early 2009 or later)
• MacBook Pro (13-inch, Mid-2009 or later),
• MacBook Pro (15-inch or 17-inch, Mid/Late 2007 or later)
• MacBook Air (Late 2008 or later)
• Mac mini (Early 2009 or later)
• Mac Pro (Early 2008 or later)
• Xserve (Early 2009)

Your Mac also needs:

• OS X Mountain Lion, Lion, or Snow Leopard v10.6.8 already installed
• 2 GB or more of memory
• 8 GB or more of available space

The Macbook Air is Apple's ultraportable notebooks with an 11 and 13 inch models.

The 11 inch Macbook Air's dimensions are:

• Height: 0.11-0.68 inch (0.3-1.7 cm)
• Width: 11.8 inches (30 cm)
• Depth: 7.56 inches (19.2 cm)
• Weight: 2.38 pounds (1.08 kg)1

Visit apple's website for more detailed specs.
https://www.apple.com/macbookair/specs.html

It's a good product but has it's limitation in terms of no CD/DVD drive, lack of USB ports, quite a small hard drive (80 GB as opposed to 500GB for a low end Macbook Pro), less RAM and smaller screen (11.3 inch as opposed to 13 inch for a Macbook Pro). For another 200 dollars you could buy a macbook pro which has higher specs.

go to system prefs/keyboard/keyboard shortcuts/keyboard and text input and check the boxes related to input sources and/or

1. Open System Preferences and click International to display its preferences.
2. Click the Language tab.
3. In the Languages pane, drag your preferred language to the top of the list.
4. Restart your Mac or log out and log back in to apply the language throughout your system.

In sound system preferences when the external mic is plugged in, there is a drop down menu in the input tab that says "Use the audio port for:" make sure it says input.

hello , your problem, maybe simple, I would say for example, there is a little cable that connect the mic to logic board, or in worst case you mic is damaged from intern. I think that the best thing that you can do is bring you macbook air and go to an apple store. you can buy some microphone on usb if u want

Have a look down the jack socket where you would plug in speakers or headphones - is there a bright red light?
If there is it means that audio is being routed through the digital output not the analogue (which includes the internal speakers)
Go to system prefs and check on Sound - last icon in the second row.
There should be at least three output options listed, digital, line out and internal speakers. check Internal speakers and that should be it.
However. Just lately I have seen 2 white macbooks that have only DIgital listed and have been unable to fix it.

Later MacBook (Pro) use a mini-DVI connector that does not pass analog needed for composite or S-video. Was yours ever working? And most DVI connectors do not pass sound as seen by your cabling. You cannot detect display through RCA. You just set it in Sys Prefs :: Displays, try some other settings, although your seem right.
I have a white early-2009 MacBook and mini-DVI to HDMI adapter (monoprice <$10) and HDMI cable and have not connected the TOS-link for sound, yet--just slideshows at 1920x1080. You will get a much better picture digitally. -Ken

I hate to break it to you, but it sounds like a hardware issue. Have you tried going into System Preferences yet? If not, go to System Prefs>Sound>Output tab and then check the speaker balance. If the slider is in the middle, then it definitely sounds like a hardware issue.
I'm going to guess you've had your MBP for a while now, which would mean that something inside like a speaker wire could have gotten knocked around enough to just fall off, or loosen a connecter just enough to make the speaker not work. That is, of course, if it is not System Prefs. Let me know how it goes.