Constant Directivity behavior, without diffraction

The goal of a horn or waveguide is to control the sound radiation of a device (tweeter or compression driver).

When a directivity is not constant, the device loose more and more coverage when the frequency goes up, the polar aka the energy in dB relative to the angle of radiation show us the problem :

On this polar map, that represents how the sound energy radiates, we can see it become tightened after 5kHz. The listening experience will be a speaker that sounds “tiny” and incoherence because there is a radiation incoherence according to frequency.

If we solve it we can have a coherent sound and a wide soundstage, thanks to constant directivity, absence of midrange narrowing/beaming and with a good integration (directivity match at crossover, space between center to center according to crossover wave-length… as seen here).

The ideal response should looks like:

It’s completely straight and the yellow color (-6dB) define the coverage angle in degrees, of course a speaker cannot be straight on all this bandwidth :

• On bottom frequency it will be the end of control of the horn directly dictated by horn width.
• On top frequency it will be stopped according to the throat size (2"/1.5"/1"), tinier the throat, upper the directivity control will be push.
• On Psycko-acoustic sides is not very desired to be constant ultra hight

Two things that it’s important to not forget :

• we always choose a frequency cross-over between two devices where the radiation pattern is similar between these two elements, see here: how to implement my horn and speakers.
• the opening of the horn must be coherent with the listening distance and the listening distance must be close to the critical distance, see in next point.

Psycko-acoustic

As Dr Floyd Tooles said the directivity pushed constant very high is not very desired by the ear (understand the brain), a decay is more appreciated by the brain in high frequencies.

So a good horn will look like this, here a X-Shape 25cm on a BMS 5530:

The goal is to push the constant directivity behavior in regards to horn width and throat size upper but not ultra high, until 7/8khz.

For the low end of the control we try to cover the most of the reverberated field, so until the begining of Schroeder area more or less, so it’s depending of room size.

We will have to reduce the midrange narrowing and the midrange beaming as well as we can.

The listening experience will be a lot better in constant directivity, in a room almost half of the sound you listen is a reflection from the wall, so even if you listen alone in front of the speaker, a constant directivity horn will change everything and will bring a more natural and fidelity listening experience.

More about Psyckoacoustic here.

Technically:

We listen at a so-called critical distance where the direct field (sound coming directly from the speaker) and the reverberant field (sound that rebound on walls) is at 50/50 or 60/40.

The brain then has a time of integration to merge the two fields, time that is different according to frequency.

As we cut when horn loses its directivity and woofers become directive there is no brutal change of directivity and no problems, the main purpose is to adapt coverage to listening distance and acoustics.

More detail here : reverb