THE SPEAKER DISPERSION
Dispersion is the off-axis emission of a speaker. Speakers play because of the to-and-fro oscillation of their radiant diaphragm, which impresses the air with which it makes contact in sudden variations of pressure that are propagated at speed of 344 mt/sec. This propagation can be omnidirectional or prevailingly frontal, according to the relationship between the speaker diameter and the frequency it plays, or in short, its wavelength. Wavelength (l) is the distance a sound covers in the air in a time equal to its cycle. By formula, the relationship between the speed of sound (c) and the cycles per second, that's the frequency (f):
l = c/f = 344/f(hz)
For any circular speaker, cone or dome it doesn't matter, the transition point from an omnidirectional emission to a directional one is represented by that frequency to which half the wavelength equals the speaker diameter. This is calculable with the following formula, where speaker diameter (D) is expressed in millimeters:
f(hz) = (344/2/D)*103 = 172,000/D(mm)
For instance, taking a 165mm speaker (6.5") we'll locate its transition point at around 1Khz. This means that up to this frequency its emission will be as far as possible omnidirectional, that is it will be characterized by a good dispersion. From this frequency on, instead, its off-axis emission will become more and more damaged. For a 50mm (2") dome midrange the transition point will be locatable in around 3.5Khz and for a 25mm tweeter (1") in around 7Khz. For all, beyond these frequencies the dispersion will start to lessen, at least in theory. In reality everything would exactly work in these terms only if the diaphragm was a rigid and crushproof piston, but it's not this way.
Increasing the frequency, also increases the motion speed and with it the acceleration imparted by the coil to diaphragm. What happens, especially with cone diaphragms, is that the more external sections don't succeed in following the sudden variations of movement imposed by the coil to vertex, so the actual surface involved in emission has the tendency to decrease. With it decreases the diameter realizing therefore that, yes, the dispersion of a cone speaker decreases as the frequency increases, but less than if it were a rigid piston.
Designing a cone with proper material and shape it's possible to get a progressive uncoupling with the peripheral sections at the frequency increase, to maintain dispersion the more constant possible. What's more, since the response of a cone would have the tendency to drop at highest frequencies because of its weight, the virtual reduction of emission diameter, involving a reduction of the moving mass, also produces beneficial effects on the in-axis response of the component. There is nevertheless a collateral effect to be checked, but it concerns the designer of the speaker, rather than you who only have to choose it: if the percentage reduction of the moving mass was superior to that of the emitting surface, the emission level would unpleasantly tend to increase, introducing more serious problems of response equalization.
But how can the dispersion of a speaker condition the results of a filter network? To explain it, suppose a typical two-way system consisting of our 6.5" woofer and our 1" tweeter, with crossover frequency tuned to 2.5Khz and all the other compatibility conditions complied. If you were exactly in front of the speakers the overall response of the system would presumably be satisfactory, but trying to listen in an off-axis position — such as when driving a car — the woofer dispersion above 1Khz will be more and more lacking, to almost zero near the crossover frequency. Result: an awful hole so big in the frequency response, visible to spectrum analysis and what's worse audible to ear. It's not a crossover nor spectrum analyzer fault. It's your empty pate 'cause you hadn't considered the speaker dispersion.
Apart from this, another aspect not to be disregarded is that inherent the load reactivity