distortion in conical horns 
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snowflake
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 2004 
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Posted: 31 December 2017 at 1:11am 
https://cdn.preterhuman.net/texts/science_and_technology/physics/Waves_and_Thermodynamics/Acoustics%20%20L.%20Beranek.pdf
page 275 shows a method for deriving an equation for distortion in an exponential horn. Can anyone do similar for a conical horn? can't quite get my head round the integration Edited by snowflake  03 January 2018 at 6:15pm 

snowflake
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looks to me like Beranek omits a root2 from the denominator in his final formula. see Olson p224 where this factor is included and therefore calculated distortion levels are lower than those in Beranek.


snowflake
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think I have done it and result is more than I thought. conical horns
can take massively more max power than exponential horns of the same
length, throat and mouth size. depending on the dispersion angle and
whether you make the exponential horn as long or shorter than than the
conical, I'm getting results of between 6dB and 15dB more output for the
same distortion level. whereas with exponential horns the max output is
severely limited by the distortion produced in the horn, with a conical
horn the distortion generated in the compression driver will be far
more significant. obviously the conical horns don't present the same
loading at the low end  unless you use a synergystyle horn.


corell
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can you post a screenshot of said equation? im curious but cant open the document :)
Have you also looked at the powerlimits for a given distortion level restricted by the throat size/ compression? also, what do you mean by "unless you use a synergy style horn"? 

snowflake
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can't work out how to paste formula images in here go to http://www.hostmath.com/ and paste in the following
"exponential "\frac{50(\gamma+1)\sqrt{\rho_0.c}}{\sqrt{2}.\gamma.P_0}\sqrt{I_T}\frac{f}{f_c}(1e^{\frac{2\pi.f_c.x}c}) "square conical "\frac{50(\gamma+1)\sqrt{\rho_0.c}}{\sqrt{2}.\gamma.P_0}\sqrt{I_T}\frac{2\pi.f\sqrt{S_T}}{c.2\tan\theta}(1\frac{\sqrt{S_T}}{\sqrt{S_T}+2x\tan\theta}) "circular conical "\frac{50(\gamma+1)\sqrt{\rho_0.c}}{\sqrt{2}.\gamma.P_0}\sqrt{I_T}\frac{2\pi.f\sqrt{S_T}}{c\sqrt{\pi}\tan\theta}(1\frac{\sqrt{S_T}}{\sqrt{S_T}+\sqrt{\pi}.x\tan\theta}) I(t) at the throat is in watts per m2. theta is half the horn dispersion angle i.e angle between axis and wall. not sure there should be such a difference between the square and round conical horns  maybe I have made a mistake there. EDIT [had missed a factor of 2 out]. will try and do it for a hyperbolic horn next which should give the exponential horn (T=1) or approximate the conical horn if T>infinity EDIT [I am assured by someone with two maths degrees that the function for the hyperbolic case cannot be integrated although it may be possible to evaluate numerically for a particular value of T] Edited by snowflake  12 January 2018 at 2:03pm 

studio45
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What kind of distortion are we talking about? What's the mechanism for it?
(I presume it's not to do with the throat geometry or termination, since those can be changed easily for any given horn)


Studio45  Box Builder Commotion Soundsystem Mobile PA


snowflake
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nonlinear compression of air. don't know why the link to the pdf isn't working now. google beranek acoustics pdf. bottom of p272


snowflake
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there were errors in a couple of the formulae above  now correct I think.


snowflake
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Edited by snowflake  13 January 2018 at 11:36am 

snowflake
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comparing a square conical horn of 50 or 60 degree dispersion with an exponential horn of equal throat and mouth but a quarter of the length  this seems like a fair comparison given the very poor LF loading of the conical horn  for a given level of distortion the conical horn can transmit approximately double the power of the exponential horn. if the horns are made equal length the conical horn can transmit nearly fifty times as much due to the lower flare rate of the exponential horn near the throat.
Edited by snowflake  12 January 2018 at 2:37pm 

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