Conclusions
Conclusions
The previous research and the research conducted this summer show strong, low even harmonics inside of the clarinet bore. In some instances the even harmonics are stronger than the odds preceding them. Even in cases where the odd harmonics were higher, the even harmonics were stronger than the odds that followed and themselves outside of the clarinet. Comparing the amplitude profiles of the individual harmonics, it can be seen that at different places inside of the clarinet the amplitude changes. These amplitude envelopes are often very different. While the fundamental's amplitude may diminish, the second harmonic could be growing. This is something else that isn't noticed when pressure readings are taken outside of a clarinet, especially with a constant note with no attack and no decay. Normally, there would be one amplitude envelope describing all of the harmonics. This is because we are observing a traveling wave inside of the clarinet, not a standing wave, at a specific spot and so we can be a node of one harmonic and an antinode of another.
The most obvious trend observed with this research is that the higher the note, the more the even harmonics are at an amplitude peak at the tone holes. The odd harmonics always tend to peak at these points, but they can peak a little bit before or after the tone hole with higher notes. This seems to coincide with the higher amplitude of even harmonics in relation to the odd harmonics found outside of the clarinet in the upper register. In the lower register, where the even harmonics are actually valleys at the tone holes, the amplitude of the odd harmonics clearly dominates.
Another interesting note is that the stronger an even harmonic is outside of the clarinet, the weaker it is on the inside. Since the even harmonics are stronger outside with higher notes, then they are weaker internally as well. Weaker and stronger in this case are relative terms. Internally they relate to how much longer the even harmonics are stronger than the odds, and not actual amplitude difference. Externally it means how high their amplitudes are compared to the odd before it.
The presence of even harmonics inside of a clarinet seems to fly in the face of common sense. These harmonics have velocities that decrease when they become open to the atmosphere at the tone holes, while their pressure becomes greater. An open tone hole should allow faster moving air to come out of it and should make the pressure atmospheric, which is a gage pressure of zero. So these harmonics aren't demonstrating the expected behavior that physics would imply. Looking at C4, F4, and G4 is very interesting, though. Though these even harmonics shouldn't exist, they look exactly how they should if they did exist based on the wavelengths of their associated frequencies. In a clarinet the fundamental's wavelength is four times the distance from the mouthpiece to the tone hole, the 2nd is two times, the 3rd four thirds times and so on down the line. The harmonics would look like this from mouthpiece to hole:
These plots are shown in absolute value so that they can be compared to the plots of my own data. The odd harmonics inside of a clarinet taken from this research don't resemble the theoretical pictures very much if at all. The even harmonics, on the other hand, resemble the theoretical very much. As was previously stated, though, the even harmonics shouldn't happen, and so those theoretical drawings of the even harmonics shouldn't happen. The fact that the internal even harmonics look like the non-existent theoretical harmonics is baffling.
As of yet we have no idea why this happens, and further research and analysis is needed to determine it. Since the upper notes exhibit strong even harmonics outside of the clarinet, only notes in the lower and middle register should be tested. Maybe an even greater resolution would help, as well as multiple tests of the same notes to average the data. We have discovered something that refutes the modern thoery of clarinet sound generation and warrants investigation.