Sound escapes any gravity well

Abstract

The principle of mechanical energy conservation limits the height at which a body of mass m and initial total mechanical energy Ei can get in a uniform gravitational field g, namely hmax=Ei/mg . However, the same conservation principle does not pose any limit to the height reachable by a sound wave in a vertical column of (ideal) fluid in the same uniform gravitational field. Here, we provide two accessible proofs of a counter-intuitive result that can represent an amusing digression from the usual presentation of the topic.