# Geometry

#### The Acoustical Line-Source

You might well ask: what is an acoustic line source and how can it improve my life style? As you will now learn, we are ready to defend to the death our maxim that the line-source is the optimum acoustical configuration to accurately re-create a musical performance in your sound room.

The infinite line-source: Conceptually, the line source is like attaching a magic guitar string (one that can generate all frequencies of the audio spectrum without prejudice) to one end of infinity and attach the other end to the diametrically opposite infinity. And, as luck would have it, the string passes through your ceiling and into the floor at the precise location where you want your speaker. This would be referred to as a (most fortunate) vertical line source. Please note, we can go into the basement and into the attic where we can clip off those portions of the line that do not intersect the room without affecting the sound in the room. This is a serious point that is entertained in our full white paper.

What does the “line” do? First, all sound rays emanate at perpendiculars to the infinite line (as well as to the truncated line in your listening room). Thus, there is no vertical dispersion. Doing deep-knee bends in front of the line would have no effect on perceived sound. Since sound is dispersed only in the horizontal plane, the line source has another interesting and useful characteristic.

Is this some form of audio alchemy or magic? As one walks toward a line source, psycho-acoustically the sound does not seem to get louder. Now, without going into further technical detail let’s consider what this all means to the perceived sound in your listening room.

Spatial Characteristics of a live concert: If you were given permission to wander around a concert hall while an orchestra was playing, you would find that as you were nearer to one side of the hall you would still be able to hear the full orchestra, but the “image” of the orchestra would have a different perspective than if you sat dead-center. In beholding this skewed image, the nearer instruments would appear louder than the more distant ones, but they would not mask the latter. You would still hear them.

Can the line source duplicate the spacial characteristics of a live concert? Now, let’s consider the line-source in the sound room. Remember, its characteristics? As you walk toward it, it doesn’t appear to get louder. Stand near one line-source speaker and it doesn’t drown out its mate. In fact, you get the same type of perspective that you heard in the concert hall, where each instrument is in its proper place regardless of where you are. This is staging. The line-source emulates the staging you heard in the hall. The so called “sweet spot” (the position in your sound room where reproduction is the best) is therefore virtually your entire sound room. No “head-vices” are required to secure your ears to the optimum spot. Get up, move around, and enjoy the full glory of your sound system without a positional penalty. This is the line source.

The ugly “point source” … head vice required: For the sake of making a complete statement, at the opposite end of the geometry spectrum is the point source. Most other loudspeakers are point sources. Their characteristics are just the opposite of a line source. As you move toward the point source it becomes dramatically louder. When you are near one point -source speaker in a stereo system, you will no longer hear the other speaker because of acoustical masking. Also, energy is radiated vertically, which now opens up another bag of worms: the problem of “taming” floor and ceiling reflections.

The only listening position possible in order to obtain proper staging and spectral balance with point sources is along a line centered between the speakers. You will most likely need a “head vice” to enjoy optimum performance. In contrast, by having no perceptible masking effects, the line-source speaker avoids this problem. Why do most designers use point sources? More than likely because it is possible to make a more compact speaker that is inherently cheaper to build.

Finale: The line source geometry preserves the original staging of an orchestra with higher accuracy than any other speaker geometry.

#### The Optimum Speaker Geometry: Why “Faceted” Panels Instead of Curved Panels?

Breaking through the Illusion of the curved panel: There have been some membrane speakers introduced on the market that have a truly curved membrane in an attempt to provide smooth horizontal dispersion of sound energy. Intuitively, this approach appears to be ideal, but don’t be easily convinced. There are some serious drawbacks.

Membrane tension of the curved membrane rapidly increases with forward displacement: Consider a horizontal cross- section of a curved membrane. It appears as a sector of a circle. When the amplifier forces the membrane outward toward the listener the membrane tension increases, which is true of all membrane speakers. However, for the curved membrane, the rate at which the membrane tension increases for a given displacement is directly proportional to the included angle of the circular arc of the membrane (dispersion angle). You will see that this creates a major limitation.

Example: the rate at which the membrane tension increases for a given displacement for an arc angle of 60 degrees is twice that for a 30 degree angle. For this reason there’s a practical limit on the dispersion angle. So what? you may ask, so why is this a problem? Please read on.

Large linear excursion – the loser of a classic tug-of-war: A major problem arises on large excursions, as a “tug-of-war” is created between the weaker electrostatic forces driving the membrane versus the strong tensile strength of the membrane (mylar, for instance, has a tensile strength greater than steel on a weight-comparative basis). Which force would you bet on? In fact, at louder sound levels the movement of the curved membrane is prematurely restricted, which is in effect, peak clilpping. This results in the loss of bass response and the “thinning out” of mid frequency response. Therefore, those who would use this approach must necessarily restrict the dispersion angle to a less than optimum angle, like 30 degrees or less.

Membrane tension rapidly decreases with backward displacement: As you might expect, when the curved membrane is forced to move away from the listener, membrane tension decreases, doing so at a rate proportional to the included angle of the arc.

The results? audible distortion at higher sound levels: Thus, on large excursions, it’s possible that the membrane can lose most of its tension. When this occurs membrane movements are no longer accurately controlled. Since the forward and backward movements of the membrane have opposite effects on membrane tension, an audible non-symmetrical distortion results at higher sound levels.

Loss of electrostatic bass response: More importantly, since linear displacement is severely limited, low frequencies must be reproduced by conventional woofers and all of the high-resolution bass potentially available with electrostatic technology is lost.

What to do? The solution: Faced with the unacceptable characteristics of the curved membrane, we developed the faceted single-membrane panel. In more descriptive terms, this technology can be viewed as a piece-wise approximation of a curved surface using flat sectors (facets). By using vanishingly small margins between facets and by judiciously selecting the proper facet width and angle between facets, a smooth dispersion curve can be obtained without a vertical “picket-fence” effect. With proper design the dispersion of energy is as smooth as a curved membrane.

You might ask: Why flat membrane sectors? A flat membrane represents the most linear geometry for membrane displacements. Furthermore, the displacement characteristic is symmetrical since the membrane accumulates tension at the same rate when moving in either direction. Thus, membrane control is never lost since tension is never lost. Furthermore, the flat membrane accumulates tension at a lesser rate than the curved membrane when displaced. This means greater linear displacements with less distortion, which consequentially means excellent electrostatic bass response and natural mid-frequency response, even at high sound levels.

Results: Great electrostatic bass response with no limit on the dispersion angle: With this technology, large linear and symmetrical membrane displacements result. What’s more, there is no limit to the amount of dispersion angle that can be selected since the angle chosen does not affect speaker characteristics as in the case of the curved diaphragm. Dispersion angles ranging from negative angles (focused energy) to a full 360 degrees are possible without affecting speaker characteristics.

Finale: Full-bodied beautiful high-resolution bass is obtained without the need of conventional mass-controlled, low-resolution “woofers”. Furthermore, mids don’t tend to “thin out” at higher sound levels due to the peak-clipping effect of the curved membrane.