Horns are known to increase the efficiency of speaker drivers. It is also known that for lower frequencies the horn has to be bigger, both in its length and the size of its mouth to properly “load” the longer wavelengths of lower freuencies. So how is it that the efficiency is increased? What is being lost when a direct radiator tries to make sound without a horn or waveguide? The answer, I believe, is that the horn drastically reduces exit shock, or diffraction, as the wave travels forward into the air. From this I am implying that direct radiators are extremely diffractive devices when they are producing wavelengths significantly larger than the cone diameter.

Years ago when I was trying to design horns from scratch, me and my friend were pondering how important the length of the horn is relative to the mouth size? What happens if you have a really long exponential horn with a small driver at the throat vs another horn with the same size mouth and same flare rate, but you cut off a bunch of the throat and put a bigger driver further up the horn? You end up with a shorter horn, same size mouth, and a bigger driver. What if you just get a big driver the size of the horn mouth and throw the horn away? I will argue that you get the same bass response!

Now there is another issue that goes on with horns that use compression drivers. Compression drivers allow a better impedance match to the air so the speaker's voice coil can “feel” the air pressure building up in front of the cone and actually push into that rather than mostly just working against the mass of the cone and voice coil. Compression loading actually changes the electrical impedance of the assembly significantly.

But the horn part, what does it do? how long does it have to be? How big does the mouth have to be?

I did an experiment recently using 1“ PVC pipe as a “horn.” This is a zero flare horn. I made it 1 foot long and put a JBL 2426 H compression driver on one end and took some measurements.Having zero flare means this horn as a serious exit shock when the sound comes out the end. But there was enough length to load 1000 Hz, holding pressure in the pipe. So did I see any efficiency gains over just measuring the compression driver without any horn attached? Sadly, no. Hardly any benefit,and an added difficulty of the pipe resonating as a result of the exit shock and it's own 1 foot length. I wanted to try this because I've found that I can successfully suppress the resonance with a pre-conditioning of the signal, using a properly timed and leveled echo signal.

Comparing the output of the 1 foot PVC pipe to a good waveguide showed a dramatic loss of efficiency, both on and off axis in the lower frequencies especially. It basically didn't do any better than the bare driver.

So in summary, just getting pressure built up in front of the driver with a pipe long enough to maintain pressure down to 500 Hz doesn't really do much good if you just release it without a gradual transition to a larger opening. The opening has to be big enough to reduce the exit shock, and the transition has to be gradual enough to do the same.This is why horns have to have some length. The real target is the mouth size, and the length is whatever it takes to gradually get there. If exit shock is to be reduced it follows that some directionality will be added. The PT waveguide in this experiment is only half as long as the 1” diameter PVC pipe, but it supports the lower frequencies dramatically better. The difference in output was extrememly obvious just from listening.

A further observation from this is that any diffractive event is lossy. A highly diffractive event is highly lossy. So any time a driver is small compared to the wavelengths it is producing it MUST be very lossy. Even if the driver weighed next to nothing and the electrical efficiency was close to 100 percent, I doubt you'd get to 10 pecent actual efficiency at converting electrical power to sound power when the driver is significantly smaller than the wavelength it's trying to procude. Unless, of course, it was in a horn or waveguide.