One thing you can do is to use a program called sox – “SoX - Sound eXchange, the Swiss Army knife of audio manipulation”.
From gnome-sound-recorder you can export a recording as a .flac file, then you can get a spectrogram using sox like this:
sox yourfile.flac -n spectrogram
which creates an image file spectrogram.png showing frequencies over time.
There are probably better ways, this is just one I happened to find.