This is an acoustical spectrum analyzer app that one can get for iphones, etc.  The top left shows the pressure of the sound wave as a function of time.  The top right shows the amplitude of each frequency making up the sound wave (the spectrum).  The bottom show the frequency as vertical distance and amplitude as brightness.  It streams to the left as a function of time.  This is excellent for examining the harmonic content of voices and instruments.  Voice “fingerprints” may be examined.

Spectrum Anallysis

I need to reinforce wave interpretations. Show the amplitude of the wave as a function of time (upper left).  Show that the amplitude increases when the loudness increases.  Show the wavelength or period changes when the pitch changes.  Do some polyphonic vocalizations to see a high frequency signal on top of my normal voice wave.


Now look at the harmonic structure of my voice (in the figure upper right).  It is the same as that for standing waves on a string.  There is the lowest frequency or fundamental and other frequencies that are integer multiples of the fundamental.  Also, an open pipe produces these harmonics, but not a closed pipe, which shows only odd multiples of the fundamental.  So, I am an open pipe, not a closed pipe?

Interestingly, this standing wave property works for light trapped between two mirrors, in a laser, for example.  Here the amplitude of the wave is related to brightness and the wavelength to the color.

Quantum mechanically this harmonic structure may be seen for electrons trapped in the space between two walls.  The amplitude here is related to the chance of reaching in and grabbing the electron.


This is all “wave stuff” where the fundamental corresponds to a half wavelength fitting between two “walls.” This is what I like about physics. One concept, “waves,” can be used to make sense of a variety of phenomena.