The Internet Archive has a lot of great music from the 78 rpm era in MP3 form. This tune is the House Carpenter,an old english ballad as performed by North Carolina musician Clarence Ashley in 1930. Some versions have the unfaithful lover being escorted to hell at the end of the song. This version just has her drowning in the ocean. There are a lot more verses to this song, likely excluded to accomodate the limited running time of a 10 inch 78rpm record.

http://ia300106.us.archive.org/3/items/Carpenter/HouseCarpenter.mp3

This tune was collected by Francis J Child in his landmark work of folklore research, The English and Scottish Popular Ballads. For those of you scoring at home, this is Child ballad #243. You can find a more complete text, as well as a midi rendering of the tune, here.

Ashley resurfaced during the 1960s folk revival, and made some excellent recordings with Doc Watson, collected on CD as The Complete Folkways Recordings.