Building a Simple Clarinet

The clarinet is open at the bell end, and essentially closed at the reed end. This results in a reflection with inversion at the bell and a reflection without inversion (plus any added pressure from the mouth through the reed opening) at the reed end. These odd boundary conditions cause odd-harmonics to dominate in the clarinet spectrum. 

We noted that the ideal string equation and the ideal acoustic tube equation are essentially identical. Just as there are many refinements possible to the plucked-string model to make it more realistic, there are many possible improvements for the clarinet model. Replacing the simple reed model with a variable mass/spring/damper allows the modeling of a lip reed as is found in 

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