Foaming At The Mouth
Boy, do I wish all titles were as easy and appropriate. We're talking about a wonderful tweak I've been working with for a little while, that is acoustic absorption at the mouth of a horn. You may have seen this in some commercial horns -- the Urei studio monitors had a coaxial horn tweeter (very similar to the coaxial Altecs) and used a foam treatment around the edge of the mouth. Peavey also utilized a foam inset edge on their "Quadratic Throat Waveguide", linked is their PDF of this, yet it doesn't cover the foam but is very worth reading as a historical interest piece on horns.
As you can see, the mouth of a plain conical horn (and the vast majority of horns, overall) has a very sharp edge, where some modern horns incorporate a roundover. When a horn ends and the wavelength exceeds the pathlength on the horn, it ceases to load the compression driver and transitions from the radiation pattern defined by the horn to one of free-air radiation. At this point, the edge acts like a secondary sound source. Just as with the edges of a box loudspeaker, the more gradual you can make the transition the more benign the effect of the diffraction in the loudspeaker. With horns this transition is even more dramatic than in a box speaker, as you're not going from 180 degrees to 360 but from 90 or less degrees to a full free-air (360 degree) radiation. By making the transition gradual, a minimum of diffraction peaking takes place and you maintain the cleanest transition from the horn loaded bandwidth to the unloaded "free air" portion. The price paid for a very thorough smooth transition from loaded to unloaded is an increase of the mouth size. The pic below shows a moderate horn termination, this termination in some horns is two or three times as large.
As you probably know, it's desired to get the centers of each loudspeaker driver as close to each other as possible. This prevents pathlength differential, and ensures that the output from each driver adds to the output from the other driver(s). If you're half-wave (180 degrees) closer to one driver than the other, then the output from the two drivers will cancel each other. This is incidentally why the dispersion in a loudspeaker driver decreases with increasing frequency. At some higher frequency (shorter wavelengths) the width of a cone becomes significant relative to the wavelength and different distances from your ear to one side of the cone/dome or the other are half-wavelength (180 degrees) and thus there's a minimum of output because the wave is cancelling. The peaks and valleys caused by this are called "comb filtering" because the regular pattern of peaks and valleys looks like the fingers of a comb.
So, we have conflicting requirements. On the one hand, a big horn with a large mouth termination is desirable to allow the horn to control to the lowest frequency and transition smoothly from its defined radiation pattern into free-air radiation. The drawback is large center-center spacing, and accordingly you get smooth off-axis response from a clean mouth termination, but get cancellations and "comb filtering" of the off axis response due to the large spacing. Alternatively, you can try to use a less thorough termination of the horn, and live with the diffraction-based ripple and inconsistent off-axis low-end response, but achieve better summation behavior between the two drivers.
What To Use
Reticulated foam is a fully "open cell" foam, there are no cell walls remaining, just a ‘web'. There is also closed cell foam, which will not allow air to pass through, which retains all of the cell walls. If you do the pucker test and find a modest resistance to airflow, but not a stoppage or a lot of force required, it's suitable. Appropriate foams are often found in material packaging, I used packaging from laptop shipping boxes for mine. Thicker is generally better for this purpose, but naturally you're limited by how the foam would interact with the other speaker drivers, you don't want to absorb the wavefront from the other drivers, if you're adding it to an already well-tuned system. In some cases this may not be an issue.
So, what does it do
in the real world?
In this first example, there's a thin sleeve around the outside of an already rounded mouth. This is just a simple way of making the mouth roundback act like it is larger than it already is. In this case I noted a reduction of midrange energy outside of the coverage pattern and a slight increase in intelligibility. Foam is applied to the whole back of the horn, creating a "deadzone" for unwanted energy. The rear view better shows the circular foam applied around the mouth. This is the Oblate Spheroid Waveguide (OSWG) as in my article above.
The second example is with a "Progressive Transition" waveguide, a JBL design. In this instance, thicker foam was used as the termination of the waveguide does not have the attention paid in the OSWG. As you can see, the foam projects forward from the waveguide, acting as a lossy extension of the horn, this is a more dramatic take on the foam treatment shown above. The desired frequencies (where the horn loads effectively) are largely unaffected as their coverage is defined by the horn prior to the effort on the termination, but the frequencies around and about the cutoff of the horn (where it ceases to load) are dramatically improved. This waveguide shows a peak in the 1 to 1.2 kHz range, and the foam reduced this about 2dB on-axis, and dramatically improved the behavior off axis between 800 Hz to 1.2 kHz.