Hi, RobertSorem!
Thanks for reaching out to Microsoft Community and posting your inquiry.
When you project your device to an external monitor, the audio and video played directly from the device would be the ones projected to the external monitor. For sound received through a microphone, you might need additional accessories in order for the captured voice to be clearly heard.
If I may ask, what is the make and model of your external microphone? Can you provide us the details on the devices and each accessory involved here so we can have a mental picture on your current setup?
You might want to check further with the microphone manufacturer as to how its captured audio can be setup with the computer projection system's speaker.
Looking forward for your response.
Kind regards,
Janette_Z