Talk:Engineering Acoustics/Clarinet Acoustics

It's great that someone posted this easy-to-read but quite thorough summary of clarinet acoustics.

The equation given for the mode frequencies just before "For example, for a bore of length ..." is correct for the idealized clarinet, but it would be better to include the end correction for the length.

It would be nice if the length (L) used was equal to the length of a Bb clarinet, which is about 0.6 m. This would make the lowest resonance frequency equal to that of a concert D3, which is about 147 Hz.

A simplified equation for Z_L is Z_L = Z_C/(1 - j/(0.6ka) . This takes into account the end correction mass for an unflanged opening as given by Kinsler et al. (4th ed, p. 274) and the high frequency resistance. That may be what is used for the input impedance graph given in Figure 6.

Unfortunately, Kinsler et al. (p. 274) don't treat the closed-open cylinder, and they insist that the resonance frequencies of the tube correspond to the zeros of the impedance rather than the poles. However, it can be shown that their equation 10.2.13 works if n/2 is replaced by (2n-1)/4, which is the same as the above mentioned equation after the end correction is inserted. The trick is to note that tan(kL) = 1/tan((2n-1)pi/2 - kL) = 1/(0.6ka), so that 0.6ka is approximately equal to (2n-1)pi/2 - kL. It follows that f_n = ((2n-1)/4)c/(L+0.6a).

Thanks for the opportunity to comment, and I hope to see some discussion on this topic. Jwbeauch1 (discuss • contribs) 03:45, 28 September 2014 (UTC)

Figure 5 is not correct
There is a lot of very good information in this article. Unfortunately Figure 5 is not correct. The text says that Figure 5 shows modes 1, 3 and 5 which are the first three modes of the clarinet that are significant for moderate blowing pressure. All of the discussion is correct, but the figure is not. Figure 5 actually shows modes 1, 5, and 7. SCThompson (discuss • contribs) 15:32, 2 February 2024 (UTC)