Interview to Diffraction,
Peter Strassacker asked Joe d'Appolito (12/2005).
Could you tell us something about acoustic diffraction?
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.
Joe could you tell something about the theory?
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.
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.
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.
Figure 2: Conceptual view of 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.
Thank you Joe. I think we got a good impression what's happening.