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distortion in conical horns

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snowflake View Drop Down
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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 Confused


Edited by snowflake - 03 January 2018 at 6:15pm
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Post Options Post Options   Thanks (0) Thanks(0)   Quote snowflake Quote  Post ReplyReply Direct Link To This Post Posted: 01 January 2018 at 11:24pm
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.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote snowflake Quote  Post ReplyReply Direct Link To This Post Posted: 02 January 2018 at 1:33pm
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 synergy-style horn.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote corell Quote  Post ReplyReply Direct Link To This Post Posted: 03 January 2018 at 12:17pm
can you post a screenshot of said equation? im curious but cant open the document :)
Have you also looked at the power-limits for a given distortion level restricted by the throat size/ compression?

also, what do you mean by "unless you use a synergy style horn"?
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Post Options Post Options   Thanks (0) Thanks(0)   Quote snowflake Quote  Post ReplyReply Direct Link To This Post Posted: 03 January 2018 at 2:50pm
can't work out how to paste formula images in here Angry 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}(1-e^{\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
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Post Options Post Options   Thanks (0) Thanks(0)   Quote studio45 Quote  Post ReplyReply Direct Link To This Post Posted: 03 January 2018 at 4:11pm
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)
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Post Options Post Options   Thanks (0) Thanks(0)   Quote snowflake Quote  Post ReplyReply Direct Link To This Post Posted: 03 January 2018 at 6:20pm
non-linear compression of air. don't know why the link to the pdf isn't working now. google beranek acoustics pdf. bottom of p272
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Post Options Post Options   Thanks (0) Thanks(0)   Quote snowflake Quote  Post ReplyReply Direct Link To This Post Posted: 12 January 2018 at 2:04pm
there were errors in a couple of the formulae above - now correct I think.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote snowflake Quote  Post ReplyReply Direct Link To This Post Posted: 12 January 2018 at 2:18pm









Edited by snowflake - 13 January 2018 at 11:36am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote snowflake Quote  Post ReplyReply Direct Link To This Post Posted: 12 January 2018 at 2:30pm
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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