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Diffraction

Dr. Joseph d'Appolito Dr. Joseph D'Appolito,
Chief Engineer at Snell Acoustics,
consultant for many manufacturers
one of the most established speaker developer
Author of e.g. Testing Loudspeakers, 1998
many DIY designs
(no longer available)

Interview to Diffraction,
Peter Strassacker asked Joe d'Appolito (12/2005).
 

Peter:
Could you tell us something about acoustic diffraction?

Joe:
Here are two definitions:

Definition 1: Diffraction is the distortion of an acoustic wave front caused by the presence of an obstacle in the sound field.

Definition 2: Diffraction is the change in direction of propagation of a wave front due to the presence of an obstacle or discontinuity.

As with anything in acoustics, diffraction is wavelength dependent. For example, consider Definition 1, if the size of the object is large compared to the wavelength of the impinging wave front the distortion will be severe. In fact some of the acoustic energy will reflect back in the direction from which the wave came. If the wavelength is much longer than any dimension of the object, the wave front will pass by as if the object were not there.

Peter:
Joe could you tell something about the theory?

Joe:
Acoustic diffraction theory is very complex as it involves the solution of partial differential equations with obscure boundary conditions. In the past only very simple geometries could be analyzed. With the advent of powerful computers and finite element and boundary element analysis techniques, however, a greater understanding of the physics of diffraction has evolved. Fortunately for us the two manifestations of diffraction which most directly impact loudspeaker response and testing are relatively easy to describe. They are low-frequency spreading loss and edge diffraction. Let's look at spreading loss first.

Spreading loss:
A typical loudspeaker will have its drivers mounted on a rectangular baffle. At very low frequencies, baffle dimensions will be small compared to a wavelength. In this frequency range radiated sound easily wraps around the enclosure making the loudspeaker omni-directional. As frequency increases and baffle dimensions become comparable to the wavelength of the radiated sound, the baffle begins to act like a reflecting surface, increasing SPL in the forward direction. This is what typically happens when a loudspeaker is placed in a listening room. Interestingly, the process is the same whether it is a surface intercepting an impinging wave or a baffle reflecting a generated wave. At very high frequencies relative to baffle dimensions, just about all sound is radiating in the forward direction. Thus over the full frequency range the loudspeaker transitions from full-space to half-space radiation and the on-axis SPL doubles, that is, it increases by 6 dB.
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Figure 1: Computer simulated response of a 220 mm driver on a baffle (blue) and on a large wall (black).

Figure 1 shows the computer simulated response of an ideal 220mm driver mounted on a very large wall (half-space radiation) and compares this with the same driver mounted on a small rectangular baffle. In the latter case response begins to fall off with decreasing frequency below 2000Hz, but most of the response drop occurs over the two octaves from 200 to 1000Hz. At 100Hz response is down by 6dB relative to the 3000Hz value. In practice, room modes, surface reflections and driver response variations may partially mask spreading loss.
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Figure 2: Conceptual view of edge diffraction

Edge Diffraction:
A conceptual picture of the edge diffraction process is shown in Figure 2. The source is driven with a pure tone producing a hemispherical wave front progressing outward along the disk surface. When the wave reaches the edge of the disk it is suddenly forced to expand into a much larger volume. The original wave continues to expand outward wrapping around the disk and diffracting to the rear with no change in phase. As the wave expands from a half space into a full space various conservation laws tell us the pressure must drop. The pressure drop at disk edge, however, causes a second wave to be launched at the disk edge traveling in the forward direction. The phase of this wave is reversed relative to the original wave. One way to view this is to consider the drop in pressure to be caused by the generation of a second wave at the disk's edge with opposite polarity to the original or incident wave.

The forward propagating diffracted wave will interfere with the original wave causing response ripples as the diffracted wave alternately reinforces or diminishes the on-axis frequency response.

Peter:
Thank you Joe. I think we got a good impression what's happening.

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