Ian Stirling said:
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Search on "voice activated microphone".
Some radio equipment does this automagically.
This may be a more appropriate topic for one of the radio newsgroups.
There may be a microphone you can buy that will plug into your radio
and do what you want.
Yes, this is called VOX operation, or Voice Operated Relay. Depending on
what kind of radio you are using, there are many commercially made units
that plug into the microphone jack. If you are looking to build a circuit,
it should be fairly easy to find one on the internet or in the Amateur Radio
Handbook by the ARRL. Give those a shot.
Brian.