The simulation is very accurate as long as the participating chassis behave "ideally".
The simulation for a "soft" plastic cone or for a huge fabric midrange dome will not match reality as well as the simulation of a Be tweeter, because my simulations assume ideal drivers.
Here is a project where I simulated the complete loudspeaker in advance, compared to measurements of the finished loudspeaker - to high frequencies it becomes less accurate, because I wanted to save computing time again (my 4-core CPU likes to calculate 6 hours for such a simulation)
https://www.diy-hifi-forum.eu/forum/showthread.php?19868-El-Grico&p=282530&viewfull=1#post282530
(Please note the scaling)
View attachment 75599
Yes, the radiation pattern is due to the interaction of the drivers with the baffle.
Normalized to the on-axis frequency response shows you the absolute FR off-axis. Imagine you manage to create a dead straight on-axis FR during crossover tuning, then you have exactly what the on-axis normalized diagrams show you.
You just have to be incredibly careful not to misinterpret them, when compared to real loudspeaker. The edge diffraction is always accompanied by a dip on axis - if no attempt is made to straighten it via the crossover. As a result, the off-axis FR shows usually no or only a small sound pressure increase in the affected frequency range.
View attachment 75601
Normalized to on-axis
View attachment 75602
The normalization to the axis frequency response simply shows best whether the radiation is uniform over all angles.
For example, you can also normalize to 30°, then it doesn't look so serious, but that doesn't change the fact that the reflections of the 0° FR tonal don't match the 30° FR.
View attachment 75603
All three diagrams show basically the same thing, but with different degrees of clarity.
... and one cannot emphasize it often enough, just because a loudspeaker radiates more evenly does not automatically mean it sounds better, because that depends on the fine-tuning of the crossover.
Let's cut to the chase.
If you really want to demonstrate that baffle edge diffraction is the primary cause of the response irregularity in the off-axis response, the thing you should do with your simulator is double the baffle width, leaving the edges sharp. If the dip-followed-by-peak is in fact caused primarily by baffle edge diffraction, as you certainly seem to think, it will absolutely, positively shift to half-lower frequency. If it remains where it is, anchored to the crossover frequency, this will be compelling evidence that baffle edge diffraction is not the primary cause of the major off-axis response irregularity. And in this case, lacking any alternative hypothesis, the foregone conclusion will be that it is the result of directivity mismatch for the two drivers. What puzzles me at this juncture is why this did not occur to you, and why you did the other stuff you have done, when ostensibly you were demonstrating that baffle edge diffraction as opposed to directivity mismatch is the principal cause of the major irregularity in the off-axis response.
I fully understand the point of normalizing the off-axis response curves to the on-axis curve. This has been the normal way of showing off-axis response for about as long as the importance of the off-axis response as been generally acknowledged. In Stereophile, for example, the 3-D plots that show off-axis response have been done this way since they started doing them. But if I measure sound pressure at a particular point location (x,y,z) in space and for a given frequency and then I make some change to the baffle and I want to know how this change has affected the sound pressure at that location and frequency, I will simply want to measure the SPL at that location, using that frequency. That's all. Suppose there is actually no change in SPL at this location and given frequency but that there is a -3 dB change in the on-axis response at that frequency. If I express the SPL at the (x,y,z) point of interest as a value normalized to the on-axis response I would conclude that there has been a +3 dB change in SPL at the (x,y,z) point of interest
even though the rounding of the corner has had no measurable effect on the SPL at that (x,y,z) point.
It seemed to me that you were endeavoring to demonstrate that the diffraction ripple was the primary cause per se of the major undulations in the off-axis response of the speaker. Logically this is the way that you would go about proving that directivity mismatch is not per se the cause of the off-axis response irregularities. I.e., if you prove that C is caused primarily by B, then it follows logically that C is not caused primarily by A. This manifest logic is why I thought that you were endeavoring to demonstrate that diffraction ripple explains fully the irregularity in the off-axis response. But you didn't do exactly that. You demonstrated that by making various changes you could smooth out the response. Okay, but
demonstrating that you can smooth out the response is not the same as demonstrating that diffraction ripple all by itself can fully explain the observed response irregularity.
Something else you wrote that I want to say something about:
"The edge diffraction is always accompanied by a dip on axis - if no attempt is made to straighten it via the crossover. As a result, the off-axis FR shows usually no or only a small sound pressure increase in the affected frequency range."
Perhaps there is a language difficulty here, or perhaps this indicates an understanding that isn't as complete as might be desired. Theoretically, diffraction produces a
ripple in the response, both on-axis and off-axis, although the ripple in the off-axis response and the ripple in the on-axis response are different with respect to the location of the individual peaks and dips. To keep this simpler I will only discuss it from the standpoint of the on-axis response. When the acoustic wavefront from the driver reaches the baffle edge there is a reflection due to the abrupt change in acoustic impedance, as you are perfectly well aware. You also likely know that the reflection is opposite in phase to the incident wave, i.e., a 180-degree phase shift occurs with a soft reflection. As frequency increases starting from very low frequency and the power radiation transitions from spherical space to hemispherical space, eventually the wavelength shortens to where the distance from the driver to the baffle edge is equal to a half wavelength. If the affected driver is centered on the baffle this occurs at wavelength matching the width of the baffle. Owing to the 180-degree phase shift that is due to the distance the wave travels to reach the edge, and to the additional 180-degree phase shift that occurs in a soft reflection, the total phase shift will be 360 degrees which implies constructive interference with the wavefront that reaches the on-axis listener directly from the driver. This is the 1st peak in the diffraction ripple, which is the strongest peak or dip in the overall ripple, and which sort of sits on top of the overall baffle step, making the baffle step appear to rise more abruptly and giving it a sharp knee.
As wavelength shortens further, at twice the frequency of the 1st peak there will be a dip in the on-axis response because at this wavelength a full wave matches exactly the distance from the driver center to the baffle edge. Then at 3x the frequency of the 1st peak, another peak. At 4x the frequency of the 1st peak, the second dip. And so on. This is why it is referred to as diffraction "ripple".
Now, here is one reason not to think that diffraction ripple is the primary cause of the irregularity in the off-axis response of the speaker. If diffraction ripple were strong enough to account for the major off-axis response irregularity, diffraction ripple should likewise be evident in the on-axis response. In particular, the 1st peak should be evident at about 1.7 kHz. But in the on-axis response, we find that the response is more or less flat in this region (as it is elsewhere). As such, if diffraction is in fact a strong effect in this speaker, strong enough to be the major cause of the big undulation in the off-axis response, the strong peak that should be apparent at 1.7 kHz would have to be concealing an erstwhile dip at this frequency. Perhaps there is a dip at 1.7 kHz, concealed by the 1st peak in the diffraction ripple. But what about the other peaks in the diffraction ripple that should also be noticeable, and what about the dips that should be evident in the on-axis response, especially the one that should occur at 3.4 kHz? There is no evidence at all of diffraction ripple in the on-axis response. As such, how would it be reasonable to think that baffle edge diffraction is a sufficiently strong effect in this speaker to be the cause per se of that major dip and peak that straddle the crossover frequency in the off-axis response?
In the off-axis response, the major dip in the response immediately below the crossover frequency followed by the peak above the crossover frequency has all of the characteristics of directivity mismatch between two drivers at their interface. The dip and the peak are clearly anchored to the crossover point. Perhaps this is coincidental, as it would have to be if it were caused by diffraction ripple, but it looks like a duck, it walks like a duck, and it even quacks like a duck.
Conventional wisdom holds that the woofer should be much more directional at wavelength matching the piston diameter, compared to the tweeter at wavelength more than six times greater than the piston diameter. Is it likely that this conventional wisdom is wrong, or is it more likely that it is possible to
compensate for the directivity mismatch by making changes of the sort that you made in the simulation? If you demonstrate that it is possible to compensate for the directivity mismatch, would this be sufficient reason to assert the lack of a directivity mismatch? Isn't this what you are doing?
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