Did you see what I heard?

Spectrogram Pro is a very cool app that plots the spectrum of sounds in real time.  That is, the vertical axis is a graph of how much sound energy there is at each frequency (what we hear as pitch) and the horizontal axis is time.  In the picture above, the left half shows me whistling in the mid-range - it shows up as mainly one bright line.  Then I plucked a single string on a guitar - on the right you see a whole series of frequencies made by this vibrating string.  The lowest one is the note you hear, and all the ones above it are overtones (or harmonics), that give the sound its guitar-like flavor.  You can also see how the upper harmonics decay away more rapidly with time.  I showed this in one of my physics classes where we had recently studied Fourier transforms - this is the fancy math that is used to process the sound wave into it's component frequencies.  The fact that the app is on the iPad means you can take it anywhere, which is very handy.  It's also just plain fun to mess around with.  It costs $2.99.