edge diffraction

"Effectively, what is happening is the measurement circumstance is changing from free-field (4-pi) to half-space (2-pi) as the frequency increases and the wavelength decreases to something approaching the overall area of the baffle. This creates a response ‘step’ of about 6 dB, the frequency of the step being dependent upon the baffle area. The effect is most pronounced on-axis, as the baffle causes a beaming phenomenon like a [sic] -automobile headlight reflector."

While what is said is mostly correct, it does make one wonder:
    * How does the wave know how large the baffle is?
    * Why 6 dB?
    * Are there any other effects?
    * Are two baffles equivalent if they have the same area but vastly different dimensions, e.g. a 30 cm X 30 cm baffle vs. a 5 cm X 180 cm baffle?
In my opinion, the key to developing an intuitive or quantitative understanding of cabinet edge diffraction is by studying it primarily the time domain and resorting to the frequency domain only when absolutely necessary. Once the effect is understood in the time domain, it is easily translated to the frequency domain by using the Fourier transform.

Imagine an ideal point source hemispherical radiator mounted on the exact center of the end of a long cylindrical solid. Such a radiator will exhibit a hemispherical radiation pattern that is independent of frequency. In addition, let us suppose it exhibits minimum phase characteristics and has flat frequency response over all frequencies. If we now excite the radiator with a discrete-time impulse of duration 0.025 mS, it will move in response to the impulse and stimulate a hemispherical acoustic impulse moving away from the point source at the speed of sound. Since the radiator is perfect, the acoustic impulse will have a shape identical to the discrete-time impulse.

Everything is very easy to visualize until the edge of the impulse reaches the edge of the cylinder. When the impulse reaches the edge of the cylinder, there is a sudden loss of support as the impulse is now free to radiate behind the face of the cylinder, not just in front of it. In this way, the impulse ‘diffracts’ or ‘scatters’ behind the face of the cylinder. Interestingly, this scattering is frequency independent, but angle dependent. So if we measured the acoustic signal behind the cylinder, we would find that it is an impulse identical to the one formed by the radiator but somewhat diminished in magnitude. Now, few of us set up our favorite listening spot behind our loudspeakers, so it makes sense to try to understand what happens in front of the loudspeaker. Due to the loss of support at the edge of the cylinder, the impulse will partially collapse as some of the pressure ‘leaks’ backwards and this causes a secondary impulse to scatter in the forward direction. Like the impulse scattered behind the cylinder, the forward-scattered impulse will also be frequency independent but angle dependent. Unlike the backward-scattered impulse, though, the forward-scattered impulse will have the opposite polarity as the original impulse. Now imagine a microphone located in front of and on the cylinder axis, far away from the cylinder. What will the microphone measure? First, the impulse from the radiator will be picked up then, delayed by an amount equal to the radius of the cylinder divided by the speed of sound, the forward-scattered impulse will be measured.

Now, as stated previously, neither the forward nor the backward-scattered impulses display frequency dependence. However, taken together, the direct and forward-scattered impulses will result in frequency dependence through constructive and destructive interference. Figure 1 and Figure 2 show the time and frequency domain behavior of the impulse as measured by a microphone located in front of and on the cylinder axis, far away from the cylinder. The radius of the cylinder is 1 meter and the radiator is mounted in the center of the baffle.