Two tools for visualizing sound.
A stroboscopic tuner. You tell it which note you are aiming for, and then it will show you a red/green bar indicating how close you are coming to hitting it. Perfectly horizontal means you are in tune, sloping down is flat, and sloping up is sharp.
An FFT spectrum analyzer. You can see how the complete spectrum evolves over time.
TunerTime is not the simplest tuner to use, but it is probably the most precise, and it has features particularly useful for piano tuners.
Have questions? The manual is at http://www.galexander.org/software/tunertime/