Dear Lloyd and Sally, On consideration I need to correct two things I have written here and add a third. :) I always seem to get drawn in further than is safe when it comes to this highly complex operation. The first was my error about the 90 phase shift in the representation of the cords as a resonant device. In fact each component contributes 90 degrees, making it 180 in total. Inductance/capacitance in an electronic device and mass/tension in the cords. The second is my confusion of the visual asymmetry. The various planes to be considered resulted in my describing a "contact" asymmetry when I realise now I meant an asymmetry of the ratio of "open : closed". The cords will always contact along their whole length but the time for which they do that, will depend upon the wave shape. The most simple example is the square wave of 50% duty cycle where the cords would be in contact, (closed), for 50% of the period of the cycle, and wide open for the other 50%. The time for the transition would be very short. This is probably the only state of complete symmetry of the open/closed ratio. A departure from a 50% duty cycle would disrupt the symmetry resulting in a totally different harmonic distribution as in the case of a saw-tooth. A saw-tooth wave would have a very short period of contact and a linear rate of motion towards its fully open position which would also be very short.
I assume I do not need to mention here that the fundamental frequency of both the square wave and the saw-tooth are identical and that all that we are concerned with is the harmonic content and their relative amplitudes.
This leads into further consideration of the ultimate wave shape of the air flow. As with any filter, its performance is governed by its load. A "pi" filter, as I'm suggesting the cords represent, needs a non-reactive load in order to work effectively. While it is reasonable to imagine that nature provides the means to attain such a loading arrangement, it also appears to have provided the flexibility to distort the value of this ideal match. Such a match would also be essential to the efficient transfer of the undistorted pressure wave to the resonant areas, for without it, the all-important harmonics would be suppressed and the mis-match would reflect on the operation of the cords as an ideal filter. Thanks for your patience in allowing me to exercise my ravings once more, blame mike! :) Now where does this leave falsetto?..(shrug).. ..wafting in the breeze. I'm off to a 5 hour rehearsal, bye. Reg.
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