in the loop

[Kingaroo]

Did this phrase, referring to a circuit of information, come into use with audio recording systems? or does it predate that?

[Clanad]

Take Our Word For It says: These are American in origin and date in print from 1970 and 1976, respectively, at least so far as is currently known. In the loop, the first, simply derives from the use of loop to mean either "A sequence of control operations or activities in which each depends on the result of the previous one" or "a sequence of instructions which is executed repeatedly (usually with an operand that changes in each cycle) until some previously specified criterion is satisfied." The former comes from science and technology in general and the latter is a computing term.

In the loop came to be used in a figurative sense to mean anyone "in the know" or made part of a process, and out of the loop derives from that.
They further explain "...The first uses recorded from 1970 and 1976 are from the Sunday Telegraph and Aviation Week, respectively. The computer and scientific uses we referred to are from 1945 and 1947 (and there are actually earlier scientific and technological uses). That's plenty of time for scientific or engineering jargon to spill into the general population...