More precise calculation for Acoustic End Correction needed

[GenSoft3d]

Hi,

I am looking for a more precise calculation for determining an accurate end correction for an open-ended pipe of a relatively high fundamental frequency and am hoping someone might be able to steer me in the right direction.

Researching online I have found the general calculation of adding 0.6 times the radius (or 0.3*d) to either end but I would like to know where this "constant" is derived from as I am skeptical of it's ability to render accurate results based on the possible variations relating to a given frequency and it's resulting acoustic impedance, etc...

I was able to find a simple formula where the volume of a half-sphere derived from the diameter of the pipe is converted to a cylinder of equal volume w/ a given length which then determines the supposed end correction value, however this value is considerably less than the general 0.6*r mentioned above.

To give an idea of my experiment; I am working with a cylindrical pipe that has an outer diameter of .5", an inner diameter of .425" and am trying to determine a length that will produce the desired frequency of 17.424 kHz.

Any help would be greatly appreciated!

 

[AlephZero]

See here: http://www.fonema.se/mouthcorr/mouthcorr.htm
or here: http://arxiv.org/abs/0811.3625

 

[GenSoft3d]

Thanks a lot for those links AlephZero... that was very helpful.

That definitely answers my question as to how the 0.6*r value is determined. However I noticed that the value presented in the info provided at the second link is 0.6133 (see Table 1, pg.12) as opposed to the more general 0.6 value more commonly found in my research.

Should I assume that the 0.6133 value is more accurate? It appears that the value is the result of additional calculations that were intended to accommodate the estimation of a time-domain reflection function r(t) for higher frequencies where the expression for the modulus |R(w)| become negative when w increases. I wonder if there is an established threshold (e.g., specific frequency) where this cross-over to negative expression occurs?