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quoted from 'loudspeaker and headphone handbook' 2nd edition edited by John borwick( i thoht it was boring when i first saw it now im loving the facts and VC and magnetic circuits )_+_+_+_+_+_+_+_+_+_+_+_+_
-for large changes in volume,pressure in horn throat is not siniusoidal%2nd harmonic distortion=1.72F/Fc Itx10^-2
F=driving frequency
Fc=horn cut off
It=Intensity (w/m^2) at horn throat_+_+_+_+_+_+_+_+_+_
is this some old rule of thumb?
or still true
thanks!
Mike
Follow Ups:
Hi Mike,Borwick's book is in fact pretty good. The wonderful chapter on transducer drive mechanisms (by Stanley Kelly) and the even more wonderful chapter on electrostatic loudspeakers (by Peter J. Baxandall) alone are worth many times the price of the book. (My copy is the first edition; the 2nd edition contains only minor additions.)
But even good books could sometimes be improved by careful proofreading. The formula you cited has become an "old rule of thumb", but the reason is mainly careless copying, not faulty physics. First, the intensity should be under a square root, as it was in Beranek's book (Equation (9.33), p. 275). However, the multiplier 1.72 (1.73 in Beranek (whether it's 1.72 or 1.73 could be explained by slightly different values having been used for the characteristic impedance of air)) is wrong--it should be 1.22. Apparently, Beranek while manipulating the equations accidentally dropped the the square root of two which correctly appears in the denominator of his Equation (9.31) (1.73/Sqrt(2) = 1.22). Beranek's slightly erroneus equation (9.33) has been copied to countless other places. The correct form is as follows:
D2(%) = 1.22*f/fc*Sqrt(It)*10^-2 .
This equation appears in slightly different but correct forms in Thuras et al., "Extraneous Frequencies Generated in Air Carrying Intense Sound Waves (JASA, Vol. VI, pp. 173-180 (January, 1935)), and also in Olson (Eq. (7.20), p. 224).
It seems that the air overload phenomenon was first theoretically investigated by B. Riemann (1860) and Y. Rocard (1933). If one of the more serious enthusiasts on here (Dennis? Steve? Bruce? anyone?) happens to have copies of the papers by these early investigators, I would be very interested in getting a copy.
Riemann's paper referred to above, "Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite" (Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, No. 8, ss. 43-65 (1860)), is available as a .pdf transcription at:http://www.emis.de/classics/Riemann/Welle.pdf
yeah it has a HUGE electrostatic speaker chapterif i was interested in those i would be very super happy!
im just borrowing the boook out of public library.
im interested in klippels ideas for non linear driver behaviour stuff
cheers!
In most cases, non-linearity in mid/hf horn throats occurs at very high SPLs, above what a home user would be able to tolerate. This is another reason that many high-end mid horns went to 3" drivers and throats to minimize the problem at normal SPLs (normal for home horns that is).
'Quacking' is well known in CD horns at high volumes.
"Everything should be as simple as possible, but no simpler"-Einstein
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