ttonon Posted October 17, 2010 Share Posted October 17, 2010 Hi Dana, I must apologize for an error I made in my last post. My statement that "any deviation from sinusoidal motion of the reed tongue would necessarily be caused by the excitation of multiple vibrational modes of the tongue" is incorrect, and arose from my own confusion between the time and space dimensions. For my own benefit and for our discussion, I think it's best to keep in mind differences between the time dependent motion (frequency spectrum) of the vibrating reed tongue, the spatial dependency of the tongue's beam mode of deflection, and both the frequency spectrum and spatial dependency of the pressure pulses in the acoustical sound field of the air vibration. I attached one of Cottingham's short papers on the subject, which I think illustrates many of these processes. I haven't used attachments before, and I hope it works. Anyway, note Figure 3, which shows the time dependency of the vibrating tongue at normal blowing amplitude, and at least by eye, illustrates a very smooth sinusoidal behavior. This figure also shows the time dependency of pressure pulses at a point upstream of the tongue, and at a point downstream, in the reed cavity. The point upstream clearly shows distinctive pressure pulses associated with the on-off valve effect of the tongue, and the point downstream illustrates how complex resulting air pressure pulses can become within the reed cavity. The tongue, in its up and down motion through the slot, not only imparts pressure pulses to the acoustic field, but as you recognize, also experiences forces from the resulting complex air motion about the tongue. These aerodynamic forces, in principle, do affect the time dependency of the tongue's motion, and also tend to excite higher modal (spatial) vibration in the tongue. Thus, Figure 4 shows the spectrum of the time dependency of the tongue's motion, for a blowing pressure that is significantly larger than that normally used. This figure indeed shows the presence of higher harmonics in the tongue's time dependent motion, but, keeping in mind that the ordinate is expressed as a log scale, these higher harmonics are confined to only about 10 percent of the tongues motion. It seems to me that such a small alteration of the tongue's time dependent motion would have a minor effect on the main acoustic field indicated in Figure 3 - even when the reed is blown at excess pressures. Also in Figure 4 is shown an even much smaller - three orders less - contribution to the tongue's motion made by the second vibrational mode. A degree of departure from sinusoidal motion obtainable by strong over blowing is also illustrated in Figures 6a and 6b. Thus, for normally blown reeds, sinusoidal time dependency seems to be the rule, and the on-off valve effect defines the origin of the acoustic field. Although it may be true that an extremely loudly blown reed tongue would experience time dependent motion significantly differing (say, at most, up to 20 %) from sinusoidal, the on-off valve effect will still be a major influence on the resulting acoustic field. Best regards, Tom Quote Link to comment Share on other sites More sharing options...
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