What does the 3/8" rounding of the side edges achieve?
As the story around the Encore measurement is developing with the measurement of a "golden sample" developed by GR-Research in the near future, it makes sense for me to create further simulations.
There seems to be some controversy as to what
effect the rounding of the speaker side edges with a 3/8'' radius has on horizontal sound radiation.
It is therefore appropriate to answer this question/controversy by simulation.
In
post#80 I had written something about it, but used a very rough model. This will be corrected in the following.
I have refined my simulation of the Encore and tried to get as close as possible to the real chassis - as good as possible on the basis of pictures, normally the chassis are measured with a caliper. Also invested more computing time for better accuracy at higher frequencies.
The first step is to compare the real Encore ASR measurement (with 1/6 oct smoothing) with the simulation (Simu crossover
[email protected]).
The simulation uses 15° steps, the ASR measurement 10° steps. Therefore only the appropriate angles are compared (!! FR is normalized to 0° !!):
View attachment 76675
Since I could only estimate the waveguide of the tweeter from pictures, the simulation above 6kHz deviates from the real measurements (and that a fabric tweeter does not behave "ideally" at an early stage).
But the range 200Hz to 6kHz corresponds very well to the real measurements, which is sufficient to evaluate the rounding of the lateral edges.
Then let's take a look at the effects of the 3/8'' rounding.
View attachment 76685 View attachment 76686
As always, the frequency responses were normalized to the on-axis frequency response:
View attachment 76682
In the upper treble, the frequency response is slightly smoothed, otherwise there is hardly any difference. The edge diffraction shifts slightly towards higher frequencies, as the "effective" baffle is now slightly less wide.
The fact that the horizontal radiation does not change when viewed as a whole due to such a small rounding is shown most impressively by the representation of the radiation as a sonogram/spectrogram (again normalized to the on-axis frequency response):
View attachment 76684
Wouldn't rule out the possibility of hearing a difference in direct comparison. However, the sound character of the loudspeaker will not change - obviously.
Thank you for doing this. It is informative and useful. I will share a couple of thoughts.
Diffraction affects both the on-axis response and the off-axis response, and as such it is useful to be able to see how each is affected by diffraction. To explain what I mean I will refer to Amir's response plots for the X-LS Encore and for the SVS Ultra bookshelf. These two speakers share the same baffle width: 8.5" (216 mm). When you look at Amir's response plots, both of these speakers exhibit the same characteristic, telltale sign of diffraction ripple at 3.2 kHz. This characteristic, telltale sign (which I'll describe in a moment) is plainly evident in the actual response plots of both of these speakers. Yet, it is not plainly evident in your simulation plots, because
in your simulation plots it is not possible to see how the on-axis response is affected by diffraction. Furthermore, the actual effect of diffraction in the off-axis response has been greatly exaggerated as a consequence of normalizing the off-axis response to the on-axis response.
The characteristic, telltale sign I am referring to is what I'll call a "pinch", alluding to the fact that the on-axis and off-axis responses appear to be pinched together at 3.2 kHz. This pinch is plainly evident in the actual response plots of both of those speakers. At this frequency, corresponding to wavelength equal to 2x baffle width, there is a diffraction-related dip in the on-axis response and a diffraction-related peak in the off-axis response. But in your simulation plots, instead of seeing this pinch, we see only an exaggerated peak in the off-axis response. We cannot be so confident that this peak is even due to diffraction per se because we don't have the confirmation we get when we see the pinch, i.e., when it is visually apparent that
both the on-axis response and the off-axis response are affected at this frequency in precisely the way predicted by the theoretical understanding. (And please note that while it would be easy to say something like, "if you want to see the pinch just subtract some power from the off-axis response and add it to the on-axis response", that this would be missing the point.)
The other comment I want to make is concerned with changing the position of the tweeter, i.e., moving it higher, and using the simulation to predict the effect. If you want to see the true effect of this change, you
have to look at the on-axis response. This kind of change potentially has a strong effect on the on-axis response, and there is little reason to expect it to have an appreciable effect in the off-axis response.
More than once I have suggested to people that Siegfried Linkwitz' investigation of baffle diffraction is very informative. One of the things that a careful reader of Linkwitz' writeup may notice in his sketches is the suggestion that it is advantageous for the baffle to be twice as tall as wide. (Not to suggest that this is feasible with a small bookshelf speaker.) This applies primarily in the case of a driver mounted at the center of the baffle, in which case the distance to the top and bottom edges will be exactly twice the distance to the lateral edges. The reason this works is that the ripple
peaks associated with the shorter of the two distances line up with the ripple
dips associated with the longer of the two distances. (The prominent 1st peak escapes unscathed, always.) The effect that occurs when the tweeter is located 1/3 of the way from one side edge and 2/3 of the way from the other side edge is similar. In this case the two most important distances are again in the ratio 2:1.
When a waveguide is used all of this becomes less important because the waveguide largely prevents the wavefront from illuminating the edges of the baffle. But if the investigation is concerned with small bookshelf speakers that do
not use a waveguide (or that use only a small, shallow waveguide), then diffraction ripple matters, and when so the effect of diffraction ripple on the on-axis response matters at least as much as the effect on the off-axis response.
If we consider the case where the tweeter is located equidistant from both lateral edges, the distance from the tweeter to the top edge (the vertical distance) should ideally be 1/2 or 1/4 or 1/8 or 2x or 4x the distance to the lateral edges, in order to get that same mutual cancellation effect, i.e., where the dips and peaks mutually cancel. And since it obviously is not practical (for a small bookshelf speaker) for this distance to be as great as the baffle width, it follows that the optimal solution is for the vertical distance to be 1/2 the distance to the lateral edges, i.e., 1/4 of the baffle width. For a baffle 8.5 inches wide, this distance will be 2.125" (54 mm), which is just barely adequate for a typical tweeter with a 4" flange. (This is pretty much what you did when you moved the tweeter, and if you had shown us the effect on the on-axis response ...)
For the case where the tweeter is laterally offset from the center, 1/3 of the distance from one side edge, the optimal solution is not so obvious. If the vertical distance is half of 1/3 of the distance from the side edge (i.e., 1/6 of the baffle width), then for a baffle that is 8.5" wide, the vertical distance will be 1.4" (36 mm), which won't be possible except in the case of tweeters with no flange and no waveguide. If the tweeter has a more typical 4" flange, then this doesn't work. The only indicated solution is for the vertical distance to be 4/3 the baffle width, which isn't feasible for a small bookshelf speaker. Thus, the best solution for a small bookshelf speaker might be for the tweeter to be centered between the side edges and with the vertical distance 1/4 the baffle width.
) and I brought home a pair of these...
