distortion in conical horns |
Post Reply |
Author | |
snowflake
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
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
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
|
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
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
|
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.
|
|
corell
Young Croc Joined: 19 August 2013 Location: Berlin Status: Offline Points: 1161 |
Post Options
Thanks(0)
|
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"? |
|
snowflake
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
|
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}(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 |
|
studio45
Old Croc Joined: 16 October 2007 Location: United Kingdom Status: Offline Points: 3863 |
Post Options
Thanks(0)
|
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 - Repairs & Building Commotion Soundsystem -Mobile PA
|
|
snowflake
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
|
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
|
|
snowflake
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
|
there were errors in a couple of the formulae above - now correct I think.
|
|
snowflake
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
|
Edited by snowflake - 13 January 2018 at 11:36am |
|
snowflake
Old Croc Joined: 29 December 2004 Location: Bristol Status: Offline Points: 3118 |
Post Options
Thanks(0)
|
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 |
|
Post Reply | |
Tweet |
Forum Jump | Forum Permissions You cannot post new topics in this forum You cannot reply to topics in this forum You cannot delete your posts in this forum You cannot edit your posts in this forum You cannot create polls in this forum You cannot vote in polls in this forum |