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Home » Sponsored » Pi Speakers » Speaker placement and wavefront launch (A visual representation on how walls affect the wavefront)
| Speaker placement and wavefront launch [message #69660] |
Sun, 02 October 2011 00:35  |
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Wayne Parham
Messages: 18786
Registered: January 2001
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Illuminati (33rd Degree) |
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The ideal: The constant directivity cornerhorn. In this configuration, the sound source is within 1/4λ from the apex of the corner. This makes the walls act essentially as a large waveguide, confining radiation to the angle of the walls. There is no waveform disturbance - It creates a perfect section of a purely spherical wavefront from the corner into the room.
Of course, not all rooms are suitable for constant directivity cornerhorns. Some have obstructions or entryways near the corners. Others have corners that are just too far apart. So not all rooms can support constant directivity cornerhorns.
This is a look at what other placements do to wavefront propogation. Let's start by moving the sound source slowly out from the apex of the corner, to see what happens. Where we cannot be within, 1/4λ, perhaps we can be reasonably close, but not that close. Is there any benefit in placements near boundaries? Or should speakers be placed far away, if they cannot be acoustically close, i.e. within 1/4λ.
I suppose it might be helpful to define acoustic scale. Things that are said to be acoustically close are those that are within 1/4λ of each other. Two sound sources that are acoustically close will sum as a single sound source. A boundary that is acoustically close is not a reflector, but rather a confining boundary, which is equivalent to a waveguide, with the bounding surface setting the radiating angle.
Things are acoustically distant if they are several wavelengths apart. They will not sum, but will not cancel either. They will develop interference patterns of energies and nulls, much like a checkerboard. There is also a transition region, sources beyond 1/4λ but less than about 1λ, where interference is worst at close range, but where spherical radiation emerges within a short distance. All sound sources will develop spherical radiation at large distances, and the acoustic scale sets the range.
I think it is most useful to examine the transition region between 1/4λ and 1λ, especially since it is so often found in home hifi installations. In this range, wavefront propogation, while not being as pure as acoustically close sources, does become spherical before the wavefront reaches the far walls. This is a generality, of course, but I think it's a reasonably useful one, and makes a good working definition of acoustic scale, e.g. close, distant and transition.
Note that the wavelength of 500Hz is 27". At 1kHz, it's half that, 13.5". These are important figures because this is the region where most matched-directivity (waveguide) speakers become directional. It's useful to be able to position speakers in the room where boundaries influence this range and below. So one should think in terms of one to two feet, when considering wavelengths in these illustrations.
First, examine what happens when we move the source just past the 1/4λ point, to 1/3λ from the apex of the corner. There is a mild band of reduced amplitude right down the center, and there is definite wavefront distortion but it isn't too bad except very close to the speaker.
Next, let's look at the wavefront when the source is 2/3λ from the corner. Here too, we see wavefront distortion, worse as the speaker gets further away from the walls. But move just a little ways from the speaker, and the wavefront becomes spherical. There are also two bands of reduced amplitude, one on each side.
Now let's move it to a full wavelength away. And let's look at the expansion as it develops, to get a better view of the way energy is distributed. Note that black areas are pressure minima, and color is pressure maxima.
One cycle:
Second cycle:
Third cycle:
Now, let's see the wavefront expansion through the room. It is clearly distorted up close to the speaker, and it remains that way for some distance. But the wavefront is still what I would call "pseudo-spherical" (for lack of a better word), in that it retains that basic expansion, on average.
Now let's see a typical loudspeaker placement, closer in from the side wall than from the wall behind the speaker. This speaker is 2λ from the wall behind it, and 3λ from the nearest side wall. When the speaker is placed this far from the walls, the wavefront becomes pretty fragmented. In terms of actual distance, for a 500Hz tone, this condition would exist with the speakers four feet from the back wall and six feet from the side wall.
All of these have been transition region distances, with the exception of the last one which was just past. That's the toughest placement to deal with, because the interference is worst. Ironically, it's also the one that is most popular, probably because it is "furniture friendly".
Now let's try moving the speakers much further, to minimize the influence of the reflections. Having the walls further away not only reduces the amplitude of the reflections, it also tends to make them less problematic at the center of the room, where listeners most likely will sit. As an example, this speaker is 4λ from the wall behind it, and 6λ from the nearest side wall. In terms of actual distance, for a 500Hz tone, this condition would exist with the speakers eight feet from the back wall and twelve feet from the side wall.
You can see why some audiophiles often prefer to have their speakers placed far away from walls. It does tend to make the center of the room less jumbled, the wavefront is relatively clean at some distance.
I think this series of illustrations makes another point abundantly clear, that there's another useful placement choice, to make the speakers nearer to the boundaries. They can be very distant, or they can be very close. It's the range in between that should be avoided.
Try to avoid placing speakers between 1λ and 4λ from boundaries, at least up through the midrange. Above that, directional tweeters and absorbent materials can be employed to reduce reflections. Where possible, avoid speaker-to-wall distances between two feet and eight feet.
The best approach is clearly to use constant directivity cornerhorns. But where that's not possible, if even the speakers can be kept within a wavelength or so, this is helpful, and makes relatively clean wavefront propogation in the listening area. But if the speakers cannot be placed this close to a boundary, it is better that they be placed far from it.
Also remember that reflections at higher frequencies are easily absorbed. Tweeter frequencies can be absorbed nicely with thin material, such as curtains. As frequency drops, the absorbent material must be thicker, or at least spaced further from the boundary. Below 1kHz or so, even fairly thick rugs won't do it, you need a foam or something that's a few inches thick. Below 500Hz, it is really tough to find things that will absorb reflections. That's where sound source locations become really important, because you can't do much to absorb the sound.
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| Re: Speaker placement and wavefront launch [message #69721 is a reply to message #69718] |
Wed, 05 October 2011 17:35  |
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Wayne Parham
Messages: 18786
Registered: January 2001
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Illuminati (33rd Degree) |
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The illustrations show radiation from a monopole source with boundary distances relative to wavelength. You're right that different frequencies create different patterns in the room, because the speaker is a fixed distance from the boundaries. But these illustrations show what the wavefront looks like if the source is 1/4λ and other multiples of a wavelength from the boundaries, whatever frequency/distance that is.
Where the source is 1/4λ from the walls or less, the sound will sum constructively with the reflection, making it more of a bounding surface than a reflector. It is simply a waveguide at that point. At greater distances (with respect to wavelength), interference patterns develop, as are shown in the other illustrations.
At low frequencies, wavelengths are large so acoustic scale is large too. What I mean by that is two sound sources (or a source and a reflector) can be separated by further distance at low frequencies and still act as one. Where things get tricky are distances beyond about 1/4λ, but at low frequencies, 1/4λ is several feet. Bass problems are usually caused by fixed standing wave room modes, a separate but very similar issue.
In the midrange, wavelengths grow shorter, yet not so small that reflections are easily trapped with absorbent materials. So the lower midrange is actually a tough range to deal with. It is nearly impossible to position a speaker in a small room where midrange quality isn't adversely affected by boundary reflections. In fact, the only configuration I know of that truly solves this problem in a small room is the constant directivity cornerhorn.
There are actually a few regions where indoors sound radiation patterns act differently. The lowest frequencies make up the pressure region, where wavelengths are long compared to room dimensions. Reflected sound sums constructively with the direct sound, so the whole room is pressurized equally. It can be thought of as slightly increasing air pressure in the room on one half cycle and slightly decreasing pressure on the other half cycle.
Above that, sound behavior enters the modal region. The walls are greater than 1/4λ from the source, so reflected sound no longer sums constructively. This is where room modes are, typically in the 20-200Hz region. Pockets of energy form, with some places in the room having strong bass energy, and others having nulls. These pockets are in different positions depending on frequency and loudspeaker placement with respect to walls. They're fixed-position standing wave modes that setup between boundaries, mostly between opposite walls and floor/ceiling, but to a lesser degree diagonally from corner to corner.
As frequency rises, above about 200Hz, the distance (both in frequency and position) between the modes grows closer and closer together, so at some point they are so close you cannot distinguish them apart. This is called dense interference, and it is the characteristic of the reverberent field, in the statistical region.
A few other things can be observed about these regions. At higher frequency, the sound is sort of an averaged energy field. Reflections are usually many wavelengths from the direct sound, so they don't really sum with the original - they modify the direct sound signal several cycles later. It's a different phenomenon. Also, higher frequencies are more directional and much easier to absorb with damping material. In fact, many things that are in every home naturally absorb sound, like carpets and drapes. Tweeters can be designed that put the sound in a pattern with constant narrow beamwidth. So higher frequencies are usually much easier to deal with than lower frequencies.
Low frequencies are harder because the long wavelengths don't lend themselves to damping with fibrous materials. The only things that are really effective at damping low frequencies are large vibrating membranes. Actually, homes with framed drywall construction act as natural sound dampers at some frequencies, because the drywall vibrates and some of the energy is therefore lost. But they don't work at all frequencies. The panel absorber has to be sized to match the frequency band of interest.
But one can use a technique that provides dense interference at low frequencies, in order to smooth the sound field in the modal region. This is what multisubs and flanking subs do. The frequencies to focus on are from 20-200Hz, because this is the modal region. A close second is the range from 200Hz to 1000Hz, where most sound sources are not directional enough to be aimed.
My take away from all this is that it is best to use directional (monopole) speakers and to place them either right up against the wall or a long way away, like over eight feet. The best approach, in my opinion, is the constant directivity cornerhorn because it is close enough to the apex of the corner to be within 1/4λ all the way up through the midrange band. The woofer and midhorn are acoustically close to the boundaries, so they have a perfect wavefront. Only the tweeter is operating high enough to be acoustically distant, and as I said earlier, high frequencies are easily absorbed with pleated drapes or whatever. The tweeter is directional too, so that helps.
The next best thing is to have sound sources either eight feet or more from all walls, or less than about two feet from the nearest walls. This is sometimes hard to do, because the acoustic center of the sound source is often in front of the speaker, and rarely at the back. So to have the face of the speaker be (just) two feet from the rear wall means it pretty much has to be scooted back nearly against the wall. But I'd rather do that than to move it out four or five feet. Having the sound source two feet away from the boundary isn't as good as being within 1/4λ - just a few inches away - but it is better than being four or five feet out. If you can't put it at least eight feet away, it's probably best to move it right up against the wall.
That's really the point of this thread, the most important thing I wanted to point out. In having many discussions with people over the years, I find that one of the biggest misconceptions (audiophile) people have is that pulling speakers out away from walls is good practice. That is true only if the speakers are really far away from the walls, like eight to ten feet or more. If your room is 20 x 30, that's just not practical, and in this case, I see some people pulling their speakers out from the walls around four or five feet - which is probably the worst distance they could choose. That's why I wrote this, to suggest that it would be better to put their speakers right up against the wall than it is to have them four or five feet from it.
There is another solution, which I mentioned earlier. The flanking sub approach is one I developed to deal with this exact problem. Most people cannot put their speakers within 1/4λ from the nearest boundaries, so self-interference notches form as a result. Speakers on stands get this self-interference notch from the floor, and often times they are also two or three feet from the back wall, making another self-interference notch, often in the same octave, forming a big wide valley.
A solution is to overlap two sound sources spaced a couple feet apart. The two sources can be a woofer and large midrange overlapping up to ~200Hz. This is the approach taken in my cornerhorns, for example. Another way to do it is with a 2.5-way speaker, with the lower helper woofer low-passed in the ~200Hz range. Or it can be a woofer in a separate box, placed a couple feet behind and to the side of a main speaker, sub on the floor and main speaker on a stand. This is a way to separate the sound sources in all three dimensions, smoothing what would have been notches from the floor and wall behind the speakers.
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| Re: Speaker placement and wavefront launch [message #69729 is a reply to message #69728] |
Thu, 06 October 2011 00:29 |
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Wayne Parham
Messages: 18786
Registered: January 2001
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Illuminati (33rd Degree) |
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The seven π is definitely a better choice if you have the right corners, as you've rightly observed from the illustrations. You really notice the difference in the midrange. That's not to say the four π speaker is deficient in any way - it's very good too, especially when used with flanking subs. It loses little, when properly setup. But the benefits of a constant directivity cornerhorn are obvious, and the difference is noticeable. Well worth doing if you have the right room.
So what's the right room, you ask. It's not really just about size, although larger rooms almost always tend to sound better than the smaller rooms, all other things being equal. But with a constant directivity cornerhorn, you need unobstructed wall space from each corner for about six feet on each side. You also need to be able to sit behind where the forward axes cross, which means you must be able to sit back at least half the distance the wall is wide. If you have a 20 foot wall between the speakers, you have to sit at least 10 feet back, which generally means you need a pretty deep room. You don't want to sit right on the back wall either, you want to sit several feet away from the wall behind you.
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I have run into this reinforcement, cancellation and what I'll call scrambling issue with the electrostatics I have. There are specific guidelines on placement and aiming directions, but it is still largely a trial and error process to get them just right. 
