Do creatures exist which can stop their hearing at will?
Yes
Many echolocating bats use the stapedius muscle to separate the inner ear bones
when they emit their call so they are not deafened by their own call. Their ears are highly sensitive to the very frequency they are making so they need a way to protect against it. They are only deafened for 2-8ms but that is enough to protect their hearing while still being able to hear any echo.
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