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The Beveridge Audio Wave Front Technolgy (BCSS)

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Technical details
by
Arthur Vered

Part I  
    
Overview

Sometime around 1965 Harold Beveridge had conceived the idea of the Cylindrical Wave Front dispersion pattern or, as he sometimes called it, the Beveridge Cylindrical Sound System (BCSS). The desire and necessity for this novel principle derived from the limitations that all conventional systems suffer, namely, the increased directional radiation with increased audio frequency and the unacceptable sound pressure loss with increased distance from the audio source. Other, but nevertheless equally important considerations, were the desire to eliminate various distortion modes introduced by the electro-mechanical limitations inherent in conventional dynamic drivers (cones). His earlier attempts and experimentation with electrostatic transducers – the type of drivers he believed will achieve most of the desired design aims – included various modalities to deflect sound waves in one way or another. He experimented with parabolic reflectors mounted in front of horizontally placed transducers, in an attempt to deflect some of the high frequencies into the listening room. Once the idea of deflected sound took hold and proved feasible, the way, I believe, was open to envisage the idea of lens.

The step to turn the concept into practice remains enormous however. In practical terms, if we already use some reflective device in order to deflect sound waves, why not attempt at the same time to “reshape” the waves and channel them in a controlled and desired manner as well? The patented invention of the Beveridge Acoustical Lens accomplishes precisely that.

In order to better appreciate what the acoustic lens achieves, it would be useful to review the way sound waves behave and the manner in which they propagate.

Point Source v Line source
  
A pulse, a sound wave, normally has a sinusoidal shape and a duration in time, as in the following diagrams. The two main attributes of sound waves are its amplitude and its frequency. So the higher the hump
"a" in the wave 



a = amplitude 



f = frequency

the louder the amplitude, or volume. Amplitude is measured in decibels (db). The distance between two adjacent waves' peaks constitutes the frequency. It is measured in Hertz (Hz, or cycles/sec). The shorter the distance between two such peaks, (in other words the more peaks per time unit), the higher the frequency. Another practical and useful attribute to remember is that whenever the curve goes above the X (horizontal) axis - no amplitude - it is said to be in the positive phase of the wave and whenever it goes under that axis it is in the negative phase.

  
High amplitude                                        Low amplitude
  
    

 


   
Low frequency                              High frequency

Further, in- and out of phase frequencies may result in nulls and peaks, that is, when played simultaneously some frequencies will cancel - or annul  - each other while others will reinforce each other to produce selective and undesired higher acoustic energy. Two waves of the same amplitude and frequency will cancel each other when played out of phase and will reinforce each other (the acoustic output will double by 3db) when played in phase, as shown in the following diagram ("in phase" means the positive phase of both waves start precisely at the same time, "out of phase" means one wave starts precisely one half of a cycle later; any deviation in these timings results in corresponding partial peaks and nulls).


In phase = Peak

 


Out of phase = Null
(deliberately shifted half a cycle for emphasis)

Any wave-generating - or pulsating - source of a square, short rectangle or circular shape, is considered to be a point source generator of waves. Conversely, a long and narrow area is considered to be a line source. The longer it is, the closer it resembles the theoretical modus of a line source. According to some calculations, such a source approaches the behavior of a proper line when its width/length ratio is equal to, or exceeds 1:10. Where a line source is intentionally placed vertically in space, relative to the listener, it is called a vertical line source.

A conventional dynamic cone or dome speaker is a point source. Note that it is not the electromechanical principle on which a specific driver is based but its geometric shape that determines its wave dispersion characteristics. Thus, a squarish or rectangular electrostatic speaker is also a point source.

It may be easier to visualize the different pattern of waves propagated by such sources in the two-dimensional domain. Imagine a rock thrown into a pond. After the initial impact - the ripples (waves) - are formed concentrically, and in ever-growing diameters, away from the point of impact. That is, the energy it contains travels outward radially. This wave's energy is directly proportional to the time elapsed from the moment of impact. If we ignore for the moment heat loses and other such minor variables, the energy density (energy per section) of the wave is thus inversely proportional to time. When the energy contained in that wave vanishes, there are no more ripples in the water. We can thus note that:


where    E = energy
          T = time

It follows that during the time waves will travel away from the point of impact, the energy contained in those waves will decrease with distance.
  
If, on the other hand, a long straight board is thrown into the lake, the distribution pattern of the waves is different. Almost all the energy is then delivered into two straight waves traveling parallel to, and perpendicularly away from, the board, with a tiny amount being propagated radially at the ends. Again, ignoring heat loses and similar variables, the straight waves don't spread out except for a "deteration" at the ends. This produces a fairly constant energy density in the line-shaped part of the wave with respect to distance.

Unlike water waves however, audio waves travel in the three-dimensional domain, in space. It gets slightly more complex when a point source of sound radiates out in a spherical shape. The radius of this half sphere grows directly with time, and its surface depends on the radius squared, so the surface varies with the radius squared. (More to the point, it is really only half a sphere, or dome, that we're concerned with here – or about half the surface of the imaginary sphere.) Given a constant energy being distributed evenly over its surface, it's density, or the sound pressure, must vary with the inverse of the square of the distance. This is the familiar inverse square law.

 
where     P = energy density 
    D = distance

In the case of a line source that radiates energy, it travels out in a cylindrical manner (with hemispherical endcaps.) As the surface area of the cylinder is proportional to it's radius, we have that the energy density varies approximately with the inverse of the distance from the line source.

We thus find the energy loss, or sound pressure of an audio line source is exponentially smaller than that of a point source. In other words, a line source is more efficient for a given amount of sound energy.

The following Fig.1 depicts how the energy density varies with distance between two difference sound sources, a point and a line source. The red line shows a point while the blue depicts a line source. It is noted that the sound energy is more intense near its origin and it diminishes progressively faster, relative to the line source

Fig.1

The following Fig.2 depicts a section of space showing the propagation of a pulse from a line source and a point (standard) source after a unit of time.

 

Fig.2

The line source sports clear advantages over a point source in terms of efficiency but that does not mean that it is in itself an ideal sound source. To give the flavor of just one such minor drawback, consider the following side view diagram in Fig.3 of a vertical line source. The source emits waves in all directions, not all of them perpendicular to the vertical plane of the line.

 Fig.3

As can be seen, the velocity component in the radial direction of those waves traveling in a non-perpendicular trajectory is slower than the those moving straight out (cosine of the angle.) That means that a pulse will have a sharp front end and a trailing back end that deteriorates with time. However, this is not considered a major drawback.

Let's consider next the distribution pattern of acoustic energy as a function of the audio frequency.

Directionality versus pitch
  
The angle of sound dispersion narrows down with the ascendance of frequency, or pitch. This means that the high frequencies are “beamed” toward the listener into an increasingly narrower area. This is irrespective of the type of sound source employed. Many attempts have been made by loudspeaker designers to overcome this intrinsic problem. The more prevalent effort involves multiple usage of high frequency units (whether dynamic tweeters or electrostatic ones) arranged in a semi-circular array in order to cover a wider angle of the listening area. As will be discussed later with regard similar arrangement of multiple units in order to achieve a resembled line source, this layout introduces interference between units which is not easily solved. A more ingenious approach, which failed to make a commercial impact, was that of connecting two full-range dynamic cones, as depicted in Fig.4 below, connected out of phase with respect to the other. This solutions resembles to a degree the idea of a pulsating sphere, with a quassi-omnidirectional wave dispersion at most frequencies.

 

Fig.4

The above design however, is limited in frequency response at both ends of the bandwidth; the units that can reproduce that high frequency portion of the audio range (domes) cannot be mechanically linked in this fashion. Another approach, which emulates a commercial effort, was undertaken by DIY enthusiasts and offered over the net.

 Fig.5

The idea is similar to the preceding one, but uses only one driver. The original membrane is discarded and in its place a new, rigid cone is built, designed to fire into a sealed enclosure. Thus, one half of the audio wave is dispensed with but the other, available one disperses circularly ("omnidirectionally") into the room. Similar limitations of audio spectrum reproduction apply to this design as well. Due to the stiffness and steep angles of the cone shape, some distortions associated with cone break-up modes are avoided in this design.

It would appear therefore, that there is no known transducer (possibly with the exception of the air ionizing transducer – expensive, polluting and potentially a health hazard) that is able to disperse the entire audio frequency omnidirectionally, or at least uniformly at wide angles. The answer, as Harold Beveridge had shown, is to manipulate in some manner the originally planar audio waves produced by a full range transducer and channel them into desired patterns in order to achieve uniform dispersion of sound irrespective of pitch. His solution to the problem was the invention of the Beveridge acoustical lens.

The Line Source
  
As was shown above, the acoustic line source has overall advantages over that of a point source because it has better acoustic energy retention (i.e. efficiency). The two graphs below visually emphasize the difference between the two.

Both diagrams reflect the energy density distribution of a sine wave restricted to a plane. This plane could be considered the space where a listener may be located. (The energy density is related to the "intensity" of the wave at a given point.)  Fig.6 shows the result of a point source (restricted to a plane containing the point source.) The extreme energy near the point and it's rapid decay as sound propagating away from it is noted. A closely placed listener will thus hear a vastly louder signal than one located further away from the source, as the acoustic energy will decrease exponentially.

 

Fig.6

 

 Fig.7

Fig.7 depicts a line source (restricted to a plane perpendicular to the line source.) The energy is not so extreme near the source and it's decay is significantly slower than that of the point source. All listeners within the given space will receive a good signal.

Given its attributes, it is no wonder that acoustic designers have sought ways to implement a line source. Attempts to achieve this are normally confined to usage of multiple units stacked in a vertical array that resembles a line source. Such attempts are beset by inherent problems of interference. Wave patterns emitted by one unit interfere at certain frequencies with those emitted by its neighboring sibling and may lead to peaks and nulls and other undesired phenomena. These side effects usually lead to sound muddling and, in time, to aural fatigue.

An exception to this rule is the ribbon transducer in it's various forms. This transducer is normally (but not always - see Decca Ribbon for example, which is not a line but a point source) designed and built from incipience as a line source. It consists of a long aluminum ribbon suspended between a column of strong magnetic field, either behind or (as in true ribbons) on either side of the ribbon. The uniformly driven diaphragm over its entire area is a line source of smooth and distortionless characteristics. The ribbon transducers suffer though, from limited bandwidth and are restricted to reproducing middle and high frequencies only, but do so extremely well.

Apart from its spatial efficiency, loudspeaker designers turn to line source multiple drivers design, for a myriad of other reasons. One such attribute, irrespective of the sound dispersal, is the power handling capabilities. Continuous power handling is mostly dependent on a speaker ability to dissipate heat. A common way to deal with this is the use of multiple drivers, so that the heat is now radiated over a number of drivers (increased radiating surface). Since the line source is constructed from a series of drivers placed in a line, this additional benefit is achieved automatically.

Another benefit is that by using multiple drivers, irrespective of their geometric arrangement, designers can split the audio spectrum into two, or more, sections, each being reproduced by specially and carefully designed drivers for their intended band. The downside of this approach is of course the necessity to introduce band splitters, or crossover networks, themselves a source of distortion and phase shifts.

It therefore seems that for a more successful candidate - capable of (nearly) full audio range reproduction, without the tribulations of the dynamic drivers - we must turn to electrostatic transducers.

The Electrostatic Driver

In principle, the electrostatic driver is a very simple planar device, that acts like a flat piston set into motion to move air and produce sound waves. A very thin conductive membrane (normally Mylar) is stretched and suspended between two perforated electrodes (stators), which are energized by a high voltage (to the tune of several thousand volts). Applying the polarized, positive and negative phases of the audio signal to those electrodes respectively, compels the diaphragm to vibrate in accordance with the polarity switch in the audio signal. Thus, the diaphragm moves toward and away from each static plate during each half of the signal. The following Fig.8 depicts the construction of such an electrostatic panel.


    
  
Fig.8

Another depiction of the principle is illustrated below, of an actual speaker built by a DIY enthusiast.



1. Stators
  2. Spacers
       3. Diaphragm
4. Frame

As mentioned earlier, any sound generator regardless of its type of operation, will beam the high frequencies into an increasingly narrow area with increase in pitch. This is called directionality and you may have heard many audiophiles speak of the "hot spot" or "magic spot", that equidistant point in front of the two toed-in loudspeakers where they best like to sit in order to perceive the entire spectrum of frequencies. Electrostatics suffer from the same phenomenon and a number of manufacturers endeavored to address the problem. Quad for example, etched concentrical "rings" onto the electrodes of their transducers (ESL63, 998) in increasingly wider circles in order to simulate the way audio waves might have dispersed over the membrane's surface, had they hit it from behind (remember the waves created by the stone in the pond?). Below is a cut section of the ESL63, showing the rings which are activated via a delay network in order to energize the diaphragm incrementally, from its center outward.


  
Quad ESL 63

Other manufacturers have employed multiple arrays of drivers, each pointing in a slightly different angle in order to cover a wider area. Martin Logan (below) adopted a different technique, pioneered by Alexander Shackman in Britain some 40 years ago and Roger Sanders in the USA, namely, to build the entire transducer in a curved shape (about a 30o arc in ML's instance), so the higher frequencies would spread over a wider angle. Despite the technical achievement, the "sweet spot" is still present to a considerable extent.


 
Martin Logan curved radiator

All the attempts described above have limitations. In the case of the multiple panel array, interference patterns occur at certain frequencies that produce nulls or peaks (the "Venetian blinds" effect). But the main deficiency (some would say the strength) of all electrostatic drivers is that they are dipole transducers, i.e. the rear acoustic output is really exposed and "fires" into the room, but 180o out of phase with the front radiation. While this does not much affect the mid- and particularly the high frequencies  - shorter in wave-length than the physical diameter of the driver itself - the lower mid and in particular the bas frequencies tend to cancel each other at certain points. Placement in the listening room thus becomes critical, but cannot overcome the problem altogether. In order to allow the front waves to remain unaffected by the rear ones, a way must be found to get rid of the latter. Enter the loudspeaker box, or the cabinet - with its own set of disadvantages....

Why Electrostatics?

We have looked briefly at some of the reasons for the preference of electrostatic over dynamic drivers. Frequency response was one of them. But the dynamic driver is beset by a stream of other, more subtle, deficiencies. Because of its size and intrinsic structure, the dynamic cone is called upon to long back-to-front excursions, movements which introduce among other effects intermodulation distortion, various cone break-up modes and Doppler distortion. Before we attend to each of those "maladies" let's try to visualize what we're talking about. 


Cone movement: a) cone at rest - no signal.  b) cone moves forward during 
one half of the wave phase.  c) cones moves backward during the second 
half of the phase. The result is a "push-pull" motion.

 

The following animation depicts a cone "reproducing" just one frequency.

Yet the cone is required to reproduce a wide range of frequencies, all at the same time. Its actual physical movement is extremely complex and quite difficult to illustrate on paper. To simplify things, let's imagine only two frequencies being simultaneously reproduced. The higher one will be modulated onto of the lower one, diagrammatically something like this:


Note the small wave "playing" on top of the large one

Although this is not a true depiction of what happens in reality, it may nevertheless give an idea of the process. Now, imagine hundreds of such waves' "ripple" on top of each other playing simultaneously, each with its own frequency, amplitude, rise and decay. It is clear that an extremely complex process is taking place where the cone, with its relatively high mass, is required to start and stop, accelerate an decelerate, thousands of times per second and reproduce all those signals.

To aggravate matters even further, we note that the cone is driven only at it's base end, by the (invisible) coil hidden inside the magnet's structure/cavity. In contrast, the electrostatic membrane is driven across its entire surface, hence, very little "membrane break-up" occurs.

The cone's mass itself is also a problem. First, the higher it is the more energy is required to displace it for a given sound pressure. But in so doing, the cone is flexing and bending (different cone materials behave differently) and it becomes physically distorted. Second, the higher the mass, the higher the energy store, thus the longer it takes for the cone to settle after the pulse. Further, higher frequencies, of an order of less than the diameter of the cone, propagate "on the surface" of the membrane outwardly and some don't "escape" at all (for a given magnetic force on the speaker coil and a given mass of the cone attached to it, the dynamic driver will have an upper frequency limit beyond which it will not be able to vibrate any faster). Apart from the various break-up modes, the cone also suffers from resonance modes, again depending on the material and the acoustic damping employed. All these factors are illustrated by the following diagram.

Lastly the nasty Doppler effect. Due to its to-and-fro displacement, the cone plane (side-view above) varies in distance from the listener. The Doppler effect involves hearing a certain note (or pitch) at varying distances. An example would be that of an approaching car, passing by and then disappearing into the distance. The noise's volume increases as the car approaches then decreases as it drives away further from us, until it fades away completely. But together with the volume, we also get the impression of a first, decrease in its frequency, then, an increase back to its original pitch - all that despite the fact that the originator of the sound - the car - produced the same loudness and pitch and kept them constant at all times. Cones suffer from a similar effect. The cumulative effect of all these deficiencies manifest itself in perceived sound distortion and ultimately in listening fatigue.

Most of these problems could be overcome if the cone was made to travel less. But for a given sound pressure, the cone-piston needs to move a certain volume of air. To displace the same volume of air by traveling only half as much, we'd need to increase its cone area by a factor of 2. In such a case all the mentioned distortions would be halved and the sound would be cleaner. It is thus obvious that the cone area, or the total radiating area of a driver, is radically important. Electrostatics achieve this feat almost as a matter of course.

A dynamic piston of, say, 10" dia. has a typical 10mm forward displacement and an equal 10mm backward movement. That's about 4/5" total. In contrast a typical electrostatic diaphragm may move +/-0.5mm (1mm total)  - about a twentieth, and often less, than that of a cone. It's radiating area is however, correspondingly much larger. Little wonder then that electrostatics are such pure and relatively distortion-free sounding devices.

To contrast the complex motion required of a dynamic piston, here's an animation depicting the movement of the electrostatic diaphragm. It's surface motion is almost frequency independent, in as much as any frequency is reproduced by the activation of the entire membrane, not just a portion of it, as in the case of the dynamic cone.

  
  

To Box or not to Box

Note the bipolar characteristic of the wave radiation in the animation above. For every sound wave propagating forward there is an equivalent wave radiating backward and out of phase. At certain low frequencies, the waves' length becomes long enough to migrate round the edge of the transducer, meet and cancel each other. A null is produced and we don't hear those sound waves (or if we do, they are extremely diminished). With dynamic cones the problem is solved by enclosing the driver in a box, thus containing the rear waves and preventing them from interfering with the front, audible ones. This solution is not without its problems, though.

Beveridge

After briefly considering - and dismissing it as impractical - the idea of using the rear radiation in some kind of "transmission line" reinforcement of the front waves, Harold Beveridge finally adopted the concept of removing the rear waves altogether, by trapping them inside the speaker's enclosure. But trapping those waves gives rise to another set of problems, namely, cabinet flexing, or resonance . When the speaker is firing "into the cabinet" the walls flex to a certain degree (depending on material, structure) and resonate in sympathy with (some) frequency(ies) being played. The cabinet thus adds its "own voice" to that of the speaker. Bracing the inner cabinet walls and other damping methods are employed to minimize the effect but none can reduce it altogether. (Some went to the extreme of filling double-walled cabinets with sand or concrete - with excellent results. These speakers though, become "non-removable" in weight).

Since he'd been saddled - by choice - with the problem of cabinet ringing, and after optimal treatment of most of the unwanted resonance, HB decided to maximize the use of the enclosed cavity and harness it to his own purposes. The transducers he produced had a useful free air impulse response (bandwidth) down to about 55Hz. By coupling the front lens (detailed later) to the transducers, he was able to turn the internal cavity into a Helmholtz resonator that reinforced the 40Hz band, thus lowering the fundamental frequency of the entire system down into the bass region. 

[For the technically minded, the device is named after the German physicist Hermann von Helmholtz who first described it in his 1863 classic, On the Sensations of Tone as a Physiological Basis. In contrast to horns, resonator cavities resonate in sympathy with a specific, chosen frequency only, thus amplifying it. 

A Helmholtz resonator built by Rudolf Koenig as a hearing aide device, with a lowest freq. of 128Hz. Each sphere resonates at a fixed frequency, and the combined eighteen frequencies allow the hard of hearing to distinguish eighteen different tones.

The formula applies to a hollow sphere/cavity with one circular opening. Helmholtz made his of glass.

f = ( c * a^.25 ) / ( pi^1.2 * sqr( 2 * v) )

Where:
f = frequency in hertz, cycles per second
c = velocity of sound = 1130 feet/second at 72 degrees F.
a = area of circular hole in square feet = pi * diameter squared /4  (pi = 3.14159)
v = volume of the sphere in cubic feet.
Feet can be substituted for meters as long as consistency is maintained throughout. The units of length all cancel out, leaving only the units of frequency, 1/sec. The speed of sound is proportional to the square root of absolute (Kelvin) temperature.]

Resonance is a natural phenomenon that can be both enhancing and destructive. In music we try to harness it to our advantge. The ocarina (aka "sweet potato") is an example of a musical instrument that employs a Helmholtz-type resonator. Although the internal volume is constant, pitch is controlled by varying the total area of the opening(s). This is different from a flute, a clarinet, a trumpet or a church organ for instance, where the pitch is controlled by varying the length of a resonant column of air. (When trying to naturally "amplify" our voice, we bring the hands to form a "horn-like" shape around the mouth but this is no Helmholtz resonator; the hands simply limit the angle into which our voice is channeled, so more "decibles" are heard in that restricted area or direction. The palms do not resonate well since tissue and liquid are good sound inhibitors.)

There are however instances in which resonance can be destructive. We are all familiar with the "super-soprano" who can shatter a glass by singing at certain frequencies. This occurs when the glass molecules are set in motion by resonance, each augmenting the other until the cumulative force exceeds that which binds the molecules together. A similarly progressive accumulation of forces was encountered by aircraft designers, when engine vibrations set in motion a progressive chain of resonances in the aircraft's wing to the point where the flexing wing detached itself from the plane and caused it to crash (several planes were lost before the phenomenon was understood). Chilling footage taken by an aircraft company depicts a heavily flexing wing with huge "waves" propagating from its root to its tip. Apart from other sources of stress, prolonged exposure to resonance is also a contributor to "metal fatigue" and nowadays careful consideration is paid by designers to all kind of possible sources of resonance. [It may not be too comforting to know that we board and fly daily thousand of aircrafts all around the world which already have many minute, innocuous cracks in their fuselage and wings - many caused by resonance - but we do! ]

Having familiarized ourselves with the Helmholtz principle, we can understand how Beveridge turned it to his advantage. Below is a top view diagram of the Beveridge system.
 

 

The volume of air, (blue area), from the throat (narrowest point) of the lens back through the transducers' membrane and into the cavity of the speaker, form the Helmholtz resonator. The volume is thus calculated to resonate at c.40Hz. This is precisely where the response of the transducer itself starts to dwindle and where it needs most help. With the aid of the Helmholtz, the entire system's response reaches down to 40Hz and even somewhat lower. Note the Helmholtz resonator characteristic: it resonates at its designed frequency and cuts off pretty sharply below that. So does the Beveridge system.

The main function of the lens is to transform the planar waves generated by the transducer into a cylindrical wavefront dispersing the sound - and all the frequencies contained therein - uniformly, across a 180o arc. Those who read the Patents will be familiar with the way they accomplish that. It should be appreciated that a lot of thinking and development work went into the design of those lenses since many mechanical and acoustical problems had to be ironed out. For instance, despite the lenses being braced at short intervals by horizontal holders, their walls also resonate. The problem is mostly solved by using a relatively inert acoustic material. Further, the inner guides experience an equal amount of sound pressure on either side, a fact which also tends to cancel out any vibrations. The outer walls though, are only exposed to sound pressure on one side only (the inner one) through half of the membrane cycle; the other side is exposed to almost the same pressure during the second half of the cycle, which is out of phase. To that end, the outer guides' walls had to be highly reinforced with resin to render them solid.

Since the transducer itself tends to emphasize somewhat the higher frequencies, Beveridge sought to tone down this effect. He solved the problem in an ingenious way, by ignoring the final inch or so of the transducer's extremities and devised the lens to cover only part of the transducer's area. He thus traded a small amount of SPL loss for accurate, more balanced frequency response. The outer inch of the radiating area is really firing into a proximity board, the higher frequencies being directional and absorbed within the enclosure. The low frequencies, which disperse omnidirectionally, find their way out through the wave guides, thus reinforcing the low frequency component of the total sound. A nice photo of Beveridge in front of an unfinished speaker illustrates the arrangement.

 

The top, as yet unmounted transducer, reveals the back
of the lens structure. Note how much narrower it is from
the actual lower, mounted transducers. The clearance
of the lens from the transducer is less than half an inch,
enough to allow low frequencies to escape through the
wave guides.

 

The other major piece of acoustic hurdle was to design the lens so that despite its increasingly curving guides toward the outer extremities, with their associated different path lengths (see photo above), the sound should reach the lens mouth with no time delays, or phase shifts. This is where the clever piece of acoustic design comes in: the goal is achieved by employing the throat (narrowest point in the lens' guides) together with calculating an equal arc-like path for the sound waves, an arc whose base is an invisible plane stretching between the outer walls of the most extreme channels and whose middle point forms the radius of that arc. Once this arc is achieved, the waves will propagate uniformly, in phase, into the room forming the legendary 180o wavefront.

Contrary to popular conceptualization of the sound waves emanating from a loudspeaker, the acoustic propagation is not a flow of air but rather a rapid to-and-fro movement of air particles, in sympathy with the diaphragm's positive and negative cycles. It's more of a piston-like movement (of air particles) and this is the reason why the volume of air in the Beveridge system that comprises the Helmholtz resonator begins, and includes, that of the "trapped" air between the throat and the transducer (diaphragm). Note that when the diaphragm's motion is inward, "into the cabinet" phase, so are the particles of air in the wave guides, and for this purpose the membrane is a "transparent" device; the air particles in the lens move in the same direction as those behind the membrane, i.e. toward the inner enclosure. 

The pressure in the lens' throat is considerably higher than that in any other part of the lens' guides (a phenomenon that in itself can, and does, give rise to wave guide walls' flexing, had they not been thoroughly braced). On the "room side" of the throat the air particles have almost infinite room to expand, hence no pressure can accumulate. At the base of the "inward side" of the throat, adjacent to the transducer, the volume is larger than that in the throat, hence the pressure will be lower. Given that the throat narrowing is about 1/7th that of the area covered by the lens immediately adjacent to the membrane, it would appear that the momentary pressure of the air in the throat will be 7 times higher. This is not entirely the case for the law of diminishing returns is at play here. (Taking that line of thought to the extreme would mean that if we narrowed the throat to almost total closure, the pressure would raise to enormous values, but that is plainly not the case.) There are those who suggested the pressure ratio to be 10:1 in the throat as there are those who suggested that by narrowing the waves guides the system becomes a Venturi device and thereafter (at the throat's exit) it becomes a horn device. Neither is the case. The acceleration of the air particles achieved in the throat is matched by a deceleration immediately following it, due to the lens' spatial expansion. The horn effect is neutralized since the guides' walls theoretically contribute nothing to the augmentation of the sound, i.e. they don't (or shouldn't) resonate. (It is recalled that any resonant column of air must have a material around it to be set in sympathetic resonance). Also note that the dispersion angle into which the waves propagate into the room is identical - with, or without, the wave guides in place - and is determined by the compass of the outer guides' walls; the lens merely aid the uniform dispersion of the entire audio range into that angle.

The last but by no means least piece of engineering "wizardry" in Harold Beveridge's arsenal is the construction of the transducers themselves. Those who had the chance to inspect them would have noticed that the "ribs" (the horizontal prongs or tines) that flank the membrane are quite thick. Moreover, a sectional cut through one of them will reveal it to be of a trapezoid shape, the wider base facing the mylar while the narrower one faces outward. This is not incidental. That short, but widening path of the sound through the tines was chosen for several reasons. The one drawback is the fact that the minute air column "trapped" between the tines has a resonance of its own and that resonance had to be kept outside the audio spectrum (above 20KHz). The actual open air area faced by the membrane is the distance between the middle points of the trapezoidal tines. However, the electrical force exercised over the mylar is that of the wider, closer base of the trapezoid - and even wider than that since, to a point, the electrical field will follow the widening path dictated by the trapezoid shape. Thus, a wider area of the mylar will be activated than the actual air gap (which, we recall, is the middle point of the trapezoid) - as is the case in virtually all other electrostatic transducers. Neat and clever. 

We can better visualize the mechanism of the cylindrical wavefront pattern, the manner in which it propagates and the way it interacts with the listening room by employing the same "pond" simulation mentioned earlier (hydrodynamics and aerodynamics have a lot in common). It is interesting to note a few phenomena in this simulation.

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The two sound sources on each wall represent the Beveridge loudspeakers. While watching the simulation, it is worthwhile to refresh the page. Note the concentrical wave dispersion as described earlier and the way waves 'hit' the top wall and bounce back into the room. This is precisely what happens in real life, only much faster. Note also, the extremely wide area available to the listener, since almost the entire room is uniformly illuminated by the 'first arrival' sound waves, as predicted by Beveridge. No more sweet spot". (The suggested listening area is a rather conservative depiction; in reality it is wider.)

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