Acoustic Horn Design – The Easy Way (Ath4)

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F

fluid

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Joined 2009
The same phrase appears in this page, underlined in the quote

https://www.animations.physics.unsw.edu.au/jw/sound-impedance-intensity.htm#sub4

Acoustic impedance, which has the symbol Z, is the ratio of acoustic pressure p to acoustic volume flow U. (There is a close analogy with electrical impedance, the ratio of AC voltage V to current I.) The specific acoustic impedance is a ratio of acoustic pressure to specific flow, which is the same as flow per unit area, or acoustic flow velocity, u. So we define acoustic impedance Z and specific acoustic impedance z thus:

  • Z = p/U and z = p/u
In all cases, 'acoustic' refers to the oscillating component. With this proviso, we can say that
  • acoustic impedance = pressure/flow and specific acoustic impedance = pressure/velocity
The specific acoustic impedance, z, is an intensive property of a medium. We can specify the z of air or of water. The acoustic impedance Z is the property of a particular geometry and medium: we can discuss for example the Z of a particular duct filled with air. Usually, Z varies strongly when the frequency changes. The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given acoustic flow at that frequency.
 
F

fluid

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Joined 2009
mabat said:
Fluid has only showed that you copied&pasted a sentence from a basic textbook definition of the quantity
Click to expand...
I did but my main motivation was to show the rest of the information behind that one line.

I don't speak mathematics but there is a lot of it in this paper where there are different equations for rectangular or circular ducts. Maybe some who does speak it can interpret whether there is any real difference apart from how to work out the cross sectional area.

https://www.win.tue.nl/~sjoerdr/papers/VKI_Rienstra.pdf
 
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AllenB

AllenB

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Obviously below some frequency the horn expansion is going to matter more, and the shape it uses to get there, less.. and if it isn't going too far, it's the kinds of difference between cross sectional shapes which matter to us in waveguide theory, that are the ones which affect the extent to which a horn behaves as a 1P device.
 
mabat

mabat

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This is probably what are the Mode Matching techniques for but I haven't seen an example of variable cross section shape (i.e. a transition from one to another) - if it's possible at all, that's far beyond my knowledge. One can obviously find modes for circular or rectangular ducts but the transition takes all the shapes in between that are even not directly defined...

At least it can be numerically simulated - we already have all the tools for that.

(The definition of acoustic impedance is really of no help here. I guess we all saw the definition many times. That's simply not an answer. If I ask how does a car accelerace, the answer is not "it has wheels".)
 
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mabat

mabat

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aragorus said:
But how?
Click to expand...
Simulate it via Ath&ABEC, there will be no other answer I think.
With a transitioned horn I was definitely able to get very similar results (impedance-wise) to a purely circular one, without any anomalities. I didn't examine the "area expansions" - not sure exactly how and that's why I asked - I would prepare the two cases (transitioned vs circular) with exactly the same expansion rates but I don't know how.
 
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mabat

mabat

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Here's a two-boards design I can share ;)
(Not optimized in any way, it's just a quick try to see what it does.)

648 x 295 x 360 mm, 1.4" throat
front.JPG


H, V, Throat impedance:
Horiz.png
Vert.png
ThroarImp.png


Code: 
; DS8N / Ath 4.9

HornGeometry = 2
Length = 240
Throat.Diameter = 36
Throat.Angle = 0

Horn.Adapter = {
  L = 120
  k = 4
  Width = 120
  Height = 42
  SC = 0
  Segments = 10
  ZMap = 0.5,0.4,0.5,0.5
}

Horn.Part:1 = {
  L = 1
  Segments = 16
  H = {
    r0 = 50
    a0 = 30
    k = 4 
    s = 0.78
    a = 34
    n = 4
    q = 0.994222
  }
  V = {
    r0 = 30
    a0 = 5 
    k = 4
    a = 23
    s = 0.5  
    n = 4.0
    q = 0.994222
  }
  ZMap = 0.5,0.3,0.5,0.9
}

Mesh.AngularSegments = 64
Mesh.ThroatResolution = 5
Mesh.MouthResolution = 14
Mesh.InterfaceResolution = 6
Mesh.RearResolution = 25
Mesh.SubdomainSlices = -2
Mesh.InterfaceOffset = 0
Mesh.WallThickness = 10
Mesh.ZMapElementSize = 0.3,0.6,0.5,0.95

ABEC.SimType = 2
ABEC.f1 = 200 ; [Hz]
ABEC.f2 = 15000 ; [Hz]
ABEC.NumFrequencies = 40
ABEC.MeshFrequency = 1000 ; [Hz]

ABEC.Polars:SPL_H = {
  MapAngleRange = 0,180,37
  Distance = 2
}

ABEC.Polars:SPL_V = {
  MapAngleRange = 0,180,37
  Distance = 2
  Inclination = 90
}

Report = {
  Title = "DS8N - H"
  PolarData = SPL_H
  NormAngle = 0
  Width = 1400
  Height = 800
}

Output.STL = 1
Output.ABECProject = 1
 
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A

aragorus

Member
Joined 2011
I managed to get similar results retuning some circ-sym profiles I had laying around.
Yours look a bit prettier tho!
I believe adding a bit of rollback even in only the horizontal will improve things a bit.
Another observation I've had is that modifying the horizontal profile only doesn't change the vertical response much, unless something dramatic is done.

On the acoustic impedance discussion - I have not encountered a definition specifying geometry, besides that describing the area change.
Maybe my info is old, but the formulas I'm familiar with describe the change in area as a series of ducts that one pops in a matrix.
And I can't recall seeing any in more than 2D - Length and Area
And it has worked for the practical cases of designing most speakers, car exhaust silencers, etc..
 
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