A 19th-century American ballad based on a poem by Richard Monckton Milnes Houghton (1809-1885), called "I Wandered By the Brookside". It's old enough to have achieved some anonymity, and as it was a popular song, the opportunity for the words to evolve into a folk phrase is great.

The reminiscent line, which acts as the song's refrain, is "The beating of my own heart / Was all the sound I heard". The song is about a young woman waiting for her lover to meet her by a silent mill as evening falls, listening for his approach. At least in my mind, it isn't far from there to "be still my beating heart", the better to hear his footstep.