Audio-recorder is exactly what you want.

From it's launchpad entry description:

This amazing program allows you to record your favourite music and
audio to a file. It can record audio from your system's soundcard,
microphones, browsers, webcams & more. Put simply; if it plays out of
your loudspeakers you can record it.

Note that it does not record via a microphone or anything like that. Rather, it saves the data as it passes through your soundcard!

Audio-recorder is quite powerful. You can have it start/stop recording when audio data starts/stops flowing through your soundcard:

It has an advanced timer that can:
* Start, stop or pause recording at a given clock time.
* Start, stop or pause after a time period.
* Stop when the recorded file size exceeds a limit.
* Start recording on voice or sound (user can set the audio threshold).
* Stop or pause recording on "silence" (user can set the audio threshold and delay).

Suppose you have Audio-recorder start/stop recording on sound/silence. If you leave an internet radio streaming all day, then at the end of the day each song will be saved to a separate file. (assuming consecutive songs are not "mixed")

Installation:

sudo apt-add-repository ppa:osmoma/audio-recorder

sudo apt-get update

sudo apt-get install audio-recorder