Discussion Forum—A Way with Words, a fun radio show and podcast about language

If I understand the question correctly, you want to know if the origin of the verb “to sound” in the sense of measuring depth, and the noun “sound” as in SONAR are related. According to the American Heritage dictionary etymologies, they are distinct, and have distinct entries.

Sound (1) Vibrations … . comes from Middle English “soun” from Old French “son” from Latin “sonus”

Sound (4) To measure … . comes from Middle English “sounden” from Old French “sonder” from “sonde”, probably from Germanic origin.

As for the seeming “circular” definition, it is probably just a limitation of translation. There was a thing called “sonde” that was used to measure depth. The best translation for that thing is a “sounding line.”