Horn Research Update
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.