[johnk...]

I don't think there is any difference between what SL is saying and what I am saying. But just to provide a little credibility please recognize I provide much assistance to Paul V in the development of the Baffle Diffraction Simulator at the FRDC. It is still one of the most comprehensive diffractions simulators available to the DIY community, after 6 years: [Paul V.] “John specifically led me through most of the unknown and rarely understood parts of diffraction, freeing me from earlier incorrect pre-conceptions, and focusing me toward the solving of the difficult solutions with easy to comprehend examples and clear methodology.”

Anyway, there is always the long wave length/short wave length designation with diffraction that is really just confusing the physics. In reality the physics is identical regardless of frequency or wave length. Place a point source on a flat circular baffle (doesn't have to be circular). For any signal it radiates a pressure wave that will have some surface component that radiates outward from the source towards the baffle edge. Since the wave is traveling at the speed of sound it doesn’t have any idea that it is approaching the edge. When the wave reaches the edge, it is free to expand or turn around the edge; at the surface the wave velocity must remain along the surface.  When this happens, a wave of the opposite family (i.e inverted or180 degrees out of phase with the initial surface wave) is created at the edge and begins to expand outward form the edge as well. This is the diffracted wave. The strength of the diffracted wave is dependent strength of the original wave and the degree of turning. For this case, where only a front radiation source is considered, the response at any point in space will be the vector sum of the signal from the source plus the diffracted signal. The phase difference between the frequency components in the direct wave and the diffracted wave will be 180 degrees plus a shift related to the difference in path lengths. For example, far from the speaker, on axis, the direct sound would have a path of length X and the diffracted sound would have a path length of X + R where R is the radius of the circular baffle.  For very low frequency, where R is much less that a wave length it contributes only a negligible shift. For example at 40 Hz, with R = 6" the phase shift would be an additional 6 degrees. The cosine of 6 degrees is 0.9945 so the vector sum is (Direct - .9945 x diffracted) which is approximately just the direct - the diffracted signal. At a higher frequency, say where the wave length is 1 foot, the phase of the diffracted signal due to the extra path length is an additional 180 degrees. In this case, the diffracted signal and the direct sound sum in phase on axis, giving rise to the peak in the baffle step response. As the frequency continues to rise the both the phase relationship between the direct and diffracted sources, as well as the relative strengths will vary (the phase shift between 0 and 360), giving rise to the irregularities in the response at higher frequency. It  doesn't matter if you analyze this in the frequency or the time domain. The result is the same.

Now, add a rear source having exactly the same frequency response as the front source, but operating 180 degrees out of phase. The same thing happens. When the rear surface  wave reaches the baffle edge it will generate a diffraction source which is 180 degrees out of phase with the original signal. Since the rear response is the same as the front, only 180 degrees out of phase, the rear diffraction signal will be the same as the front (for the same front and rear edge treatment) but 180 degrees out of phase. These two diffraction sources will sum as vectors with a phase difference of 180 degrees plus a maximum shift of 360 x (T/W) where T is the baffle thickness and W is the wave length of the signal. As long as T is much less than W the diffraction sources will cancel at any point is space. Acoustically, T being much less that W is around a factor of 10, yielding 36 degrees. Cos of 36 degrees is 0.8, so the sum would have an amplitude of 1-0.8 = 0.2 or -14 dB. For a 1” baffle this would be at a wave length of 10” or F about 1.4k Hz.  Obviously as the baffle thickness goes to zero the diffraction cancels at all frequencies, provided the front and rear sources are identical but 180 degrees out of phase. As T gets thicker, or with something like diffraction rings, the frequency where the diffraction sources begin not canceling moves lower, assuming the sources remain of the same amplitude.

However, even for a flat baffle, 1” thick baffle, a typical driver will likely have significantly different front and rear response giving rise to different amplitude for the front and rear diffractions sources. Thus, for a flat baffle it is desirable to keep the baffle width such that the peak in the dipole response is at a frequency near the upper limit where the front and rear responses are still close to similar in amplitude. At the same time, the baffle should not be  so wide as to have the driver response still being close to symmetric, front to rear, at the frequency where the first dipole null would occur, above the dipole peak since this will result is an excessively deep notch in the response above the peak. Adding angled wings, different edge treatments, etc are all other factors which will contribute to altering the symmetry between front and rear radiation and how the diffractions sources sum. These not only affect the diffraction, but also the summation of the direct response and lead to alterations in the polar response as well.

[JohninCR]

JohnK,

Thank you very much for that detailed explanation.  I hope you will continue to frequent this circle.
Despite my love of physics I bailed out after freshman year when the professor's thick accent made
electronics "diffract" off of my ears instead of soaking in, so I need to make sure I completely understand
your post before asking more about diffraction.

I'm confident that there are some real opportunities for advancement with the physical construction of
baffles.   eg I came up with a U-baffle that is 16" deep with straight sides in which I run a full range
driver with no rearside damping material, and it doesn't exhibit resonance problems.  Likewise I think I
may be on to something good using a circular baffle and fighting the negative effects via edge geometry,
even though I understand that I need to get on the stick with measuring.  I've just been dragging my
feet, because I have so many things to measure that I'll be lost in a measurement frenzy for a while.

[johnk...]

I wanted to add one comment. In my last rather run on post I discussed only those considerations due to acoustic wave motion and diffraction. I believe you brought up the observation about the actual fluid velocity around the edge due to the antisymmetric front-rear pressure oscillations of a dipole. You are correct that around the edge of a flat baffle that velocity will be a maximum. From the ordinary acoustic approach losses are not considered and that would have no effect. The fluid velocity would simply follow the baffle surface. In the real world we have to consider viscous losses. The fluid velocity along the baffle surface must be zero and there would be a thin shear layer on the baffle surface. This causes losses and could potentially be a source of additional noise generated at the baffle edge. However, I think that for a typical midrange this is probable an insignificant source of noise. Note I call it noise, not diffraction. In any event, for a equalized dipole the the excursion goes like (1/F)^3. Thus cone velocity, and therefore the fluid velocity scales as (1/F)^2. This means that the front to back velocity around the edge will be a maximum at low frequency. Thus we Would expect any related noise to be a max at low frequency. Assuming this noise source exists, then if we measure a flat baffle dipole at 90 degrees, as long as the front and rear SPL responses are antisymmetric (same amplitude, oppsite phase) all we would observed is the noise related to the fluid velocity sloshing around the baffle edge. When we measure a dipole what we see at low frequency is a deep null at ninety degrees. Thus we can conclude that this noise either has pairs of antisymmetric sources like the wave diffraction, or is so low in amplitude so as not to have any impact on the radiated SPL response. Due to the physics of the problem, such a noise source would not be antisymmetrical leaving only the conclusion that it is too low in amplitude to make any significant contribution to the radiated SPL. It is quite possible that at subsonic frequencies with very large excursions, you might start to hear some chuffing as you do in a ported system. But at higher frequencies, since the velocity goes like (1/F)^2 this would seem to not be a realistic source of noise.

Sorry to wax on so, but I wanted to address the velocity question because it was an excellent though to consider.

[Paul W]

JohninCR,
Measurements will make your quest for the grail much easier, so go ahead and bite the bullet

Here is a straight sided 15" U-baffle like you describe (18" driver) that behaves almost exactly as it should.  In-room, without damping, it exhibits a 12db spike just below 200Hz.  The resonance is damped by a single 1/4" layer of F7 wool felt across the U.
Paul

[johnk...]

Paul,

Have you seen my article on damping U's? http://www.musicanddesign.com/NaO-II-U-frame.html

[Paul W]

John,
Yes, I saw your article earlier this week (great work!).  I haven't revisited my U in light of that info...maybe when it warms up enough to play outside.  The wool felt experiments were done last summer and it seems to work well...and it took less thickness than I thought to make a remarkable difference.
Paul

[JohninCR]

John,

Thank you so much for discussing the "noise" issue related movement at the edges.
Now that will stop nagging at me, since it's a non-issue.  I assumed that once I
digest the other post that I will be able to predict the ragged response resulting from
diffraction from, for example, Olson's example of a circular baffle mounted on the end
of a cyclinder.  I believe that once I dig into it, I can optimise a circular front view
OB that has a smooth response.

I want to pursue this tangent due to my direct comparison of the B200 on a magnet
mount with the "ring", to a B200 with the same magnet mount but a rectangular baffle.
The difference in point source sound was not subtle, and the launch from the driver AND
baffle was quite apparent with the rectangle vs dead center on the driver with the ring.


Paul,

Thanks for the push, I've just been dragging my feet because it seems like work vs building
an idea, which is fun for me.