Re: "mic does not pick up sound : 2013 macbook pro.. internal mic not working unless i plug in the headset"
Ensuring your MacBook Pro has the newest compatible MacOS update can often solve issues.
We don't know which MacOS version is installed on your 2013 macbook pro.
You can check via Apple menu > About this Mac
The newest MacOS version available for each Mac generally has the newest security updates and fixes available.
Identify your MacBook Pro model - Apple Support
says
MacBook Pro (Retina, 13-inch, Early 2013) and MacBook Pro (Retina, 15-inch, Late 2013)
Newest compatible operating system: macOS Big Sur (Newest version is macOS Big Sur 11.7.10 )
or
MacBook Pro (Retina, 13-inch, Early 2013) and MacBook Pro (Retina, 15-inch, Early 2013)
Newest compatible operating system: macOS Catalina ( Newest version is macOS Catalina 10.15.7 )
The linked articles above (for Big Sur or Catalina) have tips on how to get these McOS versions.
If you choose to update or upgrade your Mac: Please remember it is wise to back up your Mac first
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Assuming your Mac has the newest compatible MacOS version for that model installed:
Restarting your Mac (Apple menu > Restart) can often help restore order if something is not working:
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If you haven't already: You may want to go to System (Settings or Preferences) > Sound and make sure the microphone input volume level (and speaker output level) is set sufficiently (slider at least near the middle) to be heard without headphones plugged in.
(NB: If headphones have their own mic. you may have an option to choose headphones or internal microphone ?)
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Else: Apple Support's articles below may be helpful in troubleshooting:
Articles are for MacOS Big Sur, (or for accurate info you can choose your MacOS version at the top of articles).
Allow use of your microphone and audio input - Apple Support
Control access to your microphone on Mac - Apple Support