- Last Updated on Tuesday, 24 November 2015 20:12

I'm now officially a horn researcher, due to my position as a PhD student at NTNU (see my first blog post for details). I hope these pages will become filled with the results of this research.

The horn speakers shown on these pages are capable of providing sound pressure levels that may damage your hearing irreversibly. Horn speakers will sound very clean even at extremely high levels, and will not give you the "distortion warning" direct radiators provide.

The tube equipment described on these pages contain potentially lethal voltages. Do not attempt to build anything of this if you don't know what you are doing.

I ASSUME NO RESPONSIBILITY FOR THE USE OF THE INFORMATION PROVIDED ON THESE PAGES.

For the first time since 2001, I went to the European Triode Festival, ETF. This year it was in Tisvildeleje in Denmark, and it was a great success. Five of us from Norway drove for 8 hours with three cars full of horns and tube amps. And one of us took the plane from Bergen.

Since the festival has been well covered by Thomas Mayer starting here (with mentions of our system here andhere), I will not try to cover everything. So this blog post will mainly cover the system we set up in the room we had.

Below is a picture of the system on Thursday afternoon. Thomas Dunker is writing up the details of the system on the whiteboard.

A block diagram of the system is shown below (click on the image for a larger version). Thanks to Lars Tørresen for the drawing.

Sources:

- Modified Dual 701 turntable with a SME II arm and a Denon DL103 pickup (Thomas Dunker)
- Micromega Minimum DVD player as CD transport (TD)

Preamps:

- Allen Wright style RTP RIAA (Bjørn Kolbrek)
- Modified Behringer DCX2496 with external linear power supply, input selector, passive analog stages and output volume control (BK)

Power amps:

- Kenwood KA-9100 for bass duty (TD)
- 300B Push-pull amps for midrange duty (BK)
- 809 SE amps for tweeter duty (BK)
- SE 801A amps (midrange, not used due to technical problems, TD)
- SE 46 amps (tweeters, not used, TD)

Speakers:

- JBL 4560 cabinets (TD) with JBL woofers by Torbjørn Lien. The woofers were a hybrid design, described by Torbjørn as "the same diaphragm as 2220-D130, magnet as D130 but with a copper voice coil, overhung, 1/2" long, i.e. the exact same motor as D140."
- "Tentamenshorn" midrange horns, as described here. These were Thomas' horns, with his modified drivers. More about that later.
- Downscaled Iwata horns (1") with TAD 2001 drivers (TL)
- Dipole tweeters with DIY 19mm 9µ titanium foil diaphragms (TL)
- Modified Coral H100 tweeters (TL)

The tweeters were crossed in passively, and mostly provided some "air".

Several people asked for drawings for the midrange horns. We hope to be able provide that, but the drawings we've got need some work before we can make them publicly available. Please be patient.

Thomas had brought two pairs of modified Altec 288B: one pair with Neodymium magnets, giving a gap B of 2.15T, and one field coil pair that were finished just in time to ETF. We played on the first pair until mid-Friday, then we switched to the field coil version. There was perhaps not a great difference, but at least both drivers sounded great! And the FC drivers look cool too. After some hours they were not so cool, though...

Friday evening we had live music.

The system of our room mates: Thomas Mayer (amps) and Wolf von Langa (speakers).

We were not the only ones to bring measurement gear.

On saturday, Thomas Dunker and I also held a lecture on horns and horn loading. This was a quite basic lecture on the horn design philosophy of the 1920s and the benefits of horn loading, using our big midrange horn as an example.

Saturday evening we listened to Charles King's tapes for what must have been several hours. His Stellavox tape machine and low-generation tapes sounded magnificent and gave us a sound quality experience we will not soon forget.

Sunday, and time to leave.

There appears to have been some problems with the contact form. Or, apparently, the form works, but I don't get the e-mails! So if you have tried to contact me over the last couple of months and not received a response, please try again.

Higher order modes in describes the deviation from simple wave propagation in horns and sound fields in general. If the wave front in the horn is not plane, cylindrical or spherical, it can be described as a sum of mode functions. In one of my earlier blog posts, and also in the reports available under Horn Theory, I have discussed this in some more detail.

Since it appears that many believe that the existence of higher order modes in horns (often just called HOM) is a quite recent discovery, I decided to put together a compilation of references on the topic. This list will probably be updated contiously as I find more references, but here are the first ones. Some of them have URLs, but you may not have permission to download the papers from the journals. If you have access to a university library, you may be able to download them there. I will not download them for you...

V. A. Hoersch: Non-Radial Harmonic Vibrations within a Conical Horn, Phys. Rev. 25, 218–224 (1925)

Perhaps the first analysis of modes in conical horns. The boundary condition at the horn mouth is not realistic (zero pressure condition), but the analysis is valid. It illustrates that the existence of HOMs were known at a very early stage in electroacoustics.

K. Sato: On the Sound Field Due to a Conical Horn with a Source at the Vertex, Japanese Journal of Physics 5, no 3, 103-109, 1929

The sound field internal and external to a conical horn is given as an expansion in spherical harmonics (modes in spherical coordinates). Directivity plots for nearfield and farfield are given.

R. J. Alfredson: The propagation of sound in a circular duct of continuously varying cross-sectional area, Journal of Sound and Vibration, Volume 23, Issue 4, 22 August 1972, Pages 433-442

The horn is divided into short cylindrical segments, where a modal description is used to compute the sound field. Modes are matched at the discontinuities, the number of modes determined iteratively.

A. Cummings: Sound transmission in curved duct bends, J. Sound Vibr. 35, no 4, 451-477 (1974)

A modal description of the sound field in a rectangular bend. Mode functions are cosine and Bessel functions.

A. H. Benade and E. V. Jansson: On plane and spherical waves in horns with nonuniform flare. I- Theory of radiation, resonance frequencies, and mode conversion, Acoustica 31, 79-98 (1974)

The existence of HOMs and their effect on the resonance frequencies of musical instruments are discussed in general terms. Some simplified calculations. Discussion of mode conversion.

E. R. Geddes: Acoustic Waveguide Theory Revisited, J. Audio Eng. Soc. 41, no 6, 452-461 (1993)

A more detailed analysis of the Oblate Spheroidal waveguide than the original 1989 paper. The existence of HOMs in the waveguide is taken into account and analyzed.

V. Pagneux, N. Amir and J. Kergomard: A study of wave propagation in varying cross‐section waveguides by modal decomposition. Part I. Theory and validation, J. Acoust. Soc. Am. 100, 2034 (1996)

V. Pagneux, N. Amir and J. Kergomard: A study of wave propagation in varying cross‐section waveguides by modal decomposition. Part II. Results, J. Acoust. Soc. Am. 101, 2504 (1997)

V. Pagneux, N. Amir and J. Kergomard: Wave propagation in acoustic horns through modal decomposition, Transactions of the Wessex Institute, 1997

The papers by Pagneux et al descibe computational methods for the calculation of horn performance based on mode matching of the sound field. The focus is on musical instruments, but the method is of course also applicable to other horns. Axisymmetric and 2D horns are described.

S. Félix, V. Pagneux: Sound propagation in rigid bends: A multimodal approach, J. Acoust. Soc. Am. 110, 1329 (2001)

Multimodal description of sound propagation through bends in tubes.

J. A. Kemp: Theoretical and experimental study of wave propagation in brass musical instruments, PhD dissertation, University of Edinburgh, 2002

A multimodal method for computing the throat impedance and mouth volume velocity of horns. Partly based on the work of Pagneux, Amir and Kergomard.

E. Geddes: Audio Transducers, 2002

Describes mode based methods for several geometries, including the oblate spheroidal coordinate system. The measurement chapter partly describes how to measure the modal amplitudes at the mouth of a horn or other transducers.

Behler, Gottfried K.; Makarski, Michael: On the Velocity Distribution at the Interface of Horn Driver and Horn, AES Convention:116 (May 2004) Paper Number:6097

Measurement of the sound field at the interface surface between a compression driver and horn, and the decomposition of this sound field into modes described in cylindrical coordinates.

Makarski, Michael: Do Higher Order Modes at the Horn Driver's Mouth Contribute to the Sound Field of a Horn Loudspeaker?, AES Convention:117 (October 2004) Paper Number:6188

Description of how a non-planar velocity wave front at the horn throat influences the sound field at the horn mouth, and the radiated sound field.

Makarski, Michael: Tools for the Professional Development of Horn Loudspeakers, PhD thesis, RWTH Aachen, 2006

The PhD thesis contains the information from the above two articles, and more. Modal decomposition of sound fields, and modal exitation of horns are described un detail. If you want to measure HOMs, this is a good place to start.

Leo L. Beranek and Tim J. Mellow: Acoustics: Sound Fields and Transducers, Academic Press, 2012

This is an update of the classical book Acoustics by Beranek from 1954, and it's the most useful book on acoustics that I have. If you plan to buy only one book on loudspeakers and sound radiation, this is the one. (For room acoustics, noise control etc, there other books that have more information, but for a loudspeaker designer, this one is a must). It covers many analytical and semianalytical methods to calculate sound fields, many of them are based on eigenmode or eigenfunction expansions.

Fall 2013

Since I have followed the Integrated PhD programme at NTNU, I did not finish my MSc until this summer (2013), even though I started om my PhD in the summer of 2011. Anyway, my MSc is now completed, and I'm working full time on my PhD.

My MSc thesis was of course also on horns, where I extended the Modal Propagation Method to rectangular horns with asymmetries. I also did an attempt on curved horns, but that was a very complex subject, as it turned out. The modes in the bend is described by Bessel functions of non-integer and imaginary order, and I also needed to find the zeros of such functions. Not that easy... You can see the result of my work here: MSc Thesis.

This fall I started working on the modal radiation impedance of rectangular ducts. I implemented some of this in my MSc thesis, so the basic functions for computing the radiation impedance for a horn mounted in an infinite baffle are available. However, most horns are not mounted in infinite baffles. They are mounted in finite baffles, unbaffled, or placed on the floor, near walls, in real rooms. Therefore I started looking into the influence of mutual impedance.

If a surface vibrates with a certain velocity, there will be a force pressing back on this surface due to the reaction of the air the surface moves. The force will be frequency dependent, and it will be more or less out of phase with the velocity. At low frequencies, there is nearly a 90 degree phase difference between the two, and little power is radiated. At higher frequencies they fall into phase, and the source radiates with maximum efficiency. The ratio of this force to the velocity is called the radiation impedance.

If two or more surfaces are vibrating, or if a source vibrates near a hard wall, so that an image source is formed due to the "mirroring effect" of the wall, each source will generate a pressure on the other. The ratio of the pressure of one source to the velocity of the other is called the mutual radiation impedance. It has to be taken into account whenever sources are near walls, or when there are multiple sources.

In addition to mutual impedance, diffraction from the baffle edges for horns in finite baffles also creates pressure on the radiating surface. To quantify this effect is what I'm currently working on.

All these simulation models do of course have to be checked against reality. The workshop at the university has therefore built me some pretty horns to measure. They have an aluminium inner skin, and 4 layers of 3mm MDF laminated on top of that, finished with some bracing, as shown on the picture below:

Having this horn ready, I mounted it in a fairly large baffle, and measured in the anechoic chamber at the University. The test setup is shown below:

I measured both the throat impedance using the two-microphone method, and the pressure at various points.

Below is a graph of the measured throat impedance, compared to the impedance simulated with the Modal Propagation Method, using 16 modes in each direction. Seems like I'm on the right track with this method....

The deviations from the simulated impedance above 2.5kHz is first the cross-modes in the measurement tube, and then, above 4kHz, we can see the effect of the microphone spacing becoming less than half a wavelength.

This horn is intended as a 1:4 scale model of a 50Hz midbass horn. An even shorter version of it, designed to be mounted near a floor/wall intersection, is also under way. This is quite common for midbass horns, and the idea is to try out this horn at various positions in a scale model of a room.

The general rule of thumb has been that by placing a horn near a wall, one can get away with a smaller mouth. This is not necessarily the case. Below is an example. The pale (overlay) lines are the throat impedance for the horn mounted in an infinite baffle, the same as above. The darker lines shows what happens when a wall is placed near the horn (30cm from the center of the mouth, which is 35x35cm). It is actually worse than the horn in the baffle alone.

Placing the horn nearer the wall (20cm from the center of the mouth) improves the situation. And the nearer it gets, the better. Conversely, at 40cm the impedance is much more peaky than at 30cm.

But note also that the higher frequency ripple increases.

More data will be published on this later. But for the time being, it is worth keeping in mind that things are not as simple as rules of thumb may lead us to believe. Especially with horns.

Not only plane or spherical waves propagate in horns. Above a certain frequency, the wave front becomes much more complex, and this complex wave front can be described as a weighted sum of mode functions.

You may be familiar with standing waves in rooms. These standing waves can only exist at certain frequencies, and their shape is given by the so-called boundary conditions. For a room with hard walls, the boundary condition is that the velocity perpendicular to the wall should be zero. That means that the pressure has its maximum values at the walls. A room will have modes in all three directions, and the pressure at any point will be a sum of the contributions from all excited modes.

Another example of modes is the vibration of a string. A string is fixed at the ends, so the boundary condition is that the displacement should be zero at the ends. The mode functions for displacement are sine functions. Then the string can vibrate with shapes that are sums of sine functions that can fulfil the condition of zero displacement at the ends.

In horns, the pressure distribution across a cross-section can also be viewed as a sum of mode functions that meet the boundary conditions. For an axisymmetric horn, using a plane cross section, these functions can be cylindrical Bessel functions. These are the mode functions for a cylindrical tube of constant cross section. A horn can be approximated by a series of short, cylindrical tubes. At each change of cross section, the mode functions in the two tubes must be matched. The mode functions will not be the same in the two tubes. This means that a single mode coming to a change in cross section will generate a series of other modes in the following duct. This is known as mode coupling.

This fact can be used to simulate horns, by letting the wave at the throat propagate through the horn, generating new modes at each change in cross section, and letting them propagate or decay through the next part of the horn, and so on. A method to do this is described by Kemp in his thesis. During my project in Numerical Acoustics this fall (2011), I implemented this method and compared it to BEM. The report can be found here. The end result was in very good agreement with BERIM (a boundary element method for horns in infinite baffles), and much faster. I plan to make the method available, hopefully both as a little Windows executable, and as a Matlab toolbox. Update: The Matlab toolbox is available here.

Update: Spring 2012 I undertook a more detailed evaluation of the modal propagation method, to check the accuracy and computation times etc. The report can be downloaded here.

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©1999-2014 Bjørn Kolbrek