Loudspeaker Addendum
John Kormylo - ELFSOFT

• Exponential Horns
• Radial Horns
• Exponential Diaphragm
• Appendices

Much of what I had read about exponential horn speakers turned out to be wrong. The passband has little to do with the mouth and throat diameters, and almost everything to do with the length and curvature (see AppendixG). There are ripples in the response and phase distortions near the low frequency limit, and the speaker still must operate above its mechanical resonance frequency to compensate for the far field conversion.

While a horn speaker is more efficient than a simple diaphragm, it can't handle low frequencies and those are where most of the power is consumed.

When a speaker is aimed at the floor or at a wall, the gap between the enclosure and the barrier acts as a parallel plate waveguide. The resulting sound volume increases as the square root of the radius. But unlike exponential horns, there is no problem with low frequencies (see AppendixH).

Speakers use cones or domes instead of flat plates for stiffness. A cone can be treated as an exponential horn with a varying exponent. Specifically it must operate BELOW the low frequency limit for a horn to function well as a diaphragm. This is one of the reasons that cones convert to a domes at some radius.

A diaphragm shaped like an exponential horn is the stiffest shape which will operate all the way to a specific high frequency limit. In fact, one can design a large diaphragm which should work well all the way to 20 kHz. Of course, the sound produced will be very direction when the diameter exceeds one half wavelength.

One solution to the directionality problem is to aim the speaker directly upward and reflect the sound off a 45 degree cone (or half cone). There is still directionality in the vertical, but ears don't move up and down that much.

Using one speaker for the entire audio spectrum eliminates almost all of the source of distortion (assuming the diaphragm is sufficiently stiff). One problem with this solution is Doppler distortion. Specifically, the large excursions needed to produce low frequencies will cause a Doppler shift to the high frequencies (band spread). This can only be solved using multiple diaphragms.

An esthetically pleasing solution is to use a two speaker system with the high frequency speaker aimed up at a conical reflector and a low frequency speaker aimed down at the floor (radial horn). This provides perfect horizontal dispersion at all frequencies.