die away

Also, die down. Gradually diminish, fade, or subside; slowly come to an end. For example, As they moved higher up, their voices died away, or The rain seems to be dying down. The first term, from the late 1600s, today is most often applied to a diminishing sound and was originally used to describe the wind slowing down or ceasing to blow. The variant dates from the first half of the 1800s.

The verb has one meaning:

Meaning #1: become less in amount or intensity
  Synonyms: abate, let up, slack off, slack