Creating the Sweet Spot

Of all the components in a modern installed sound system, the loudspeaker remains the one item whose performance is critically dependent upon the location
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Creating the Sweet Spot

Aug 1, 2002 12:00 PM, Andrew Jones

Of all the components in a modern installed sound system, the loudspeaker remains the one item whose performance is critically dependent upon the location within and the characteristics of the listening environment. A lack of understanding of the speaker and room parameters that govern this relationship will lead to, at best, a suboptimum performance or many hours of expensive trial and error.

The discussion about loudspeakers and rooms has mainly concentrated on the influence of standing waves (because of the room boundaries) upon the position requirements for the loudspeaker and the listener. Poor positioning of either can lead to uneven, exaggerated bass performance and sound quality variation for listeners seated in different locations. When listening to stereo, it is common to have a sweet spot where the sound is optimum, and that spot can often be small, perhaps confined to one listener. This is far removed from present-day requirements of multiroom, multichannel home theater for the whole family that characterizes the current install business. Sound now must be optimized for all locations.

To fully accomplish this goal, you must consider more than just the standing-wave problem. In this article, I will examine the radiation characteristics of practical loudspeakers, which determine their perceived tonal balance in rooms. I will outline steps that can be taken at the design stage to minimize room-loudspeaker interaction. I'll also explain the features to look for in selecting loudspeakers for a given install.


Unlike an electronic device such as a DVD player or an amplifier, a loudspeaker has an output response to its input that is three-dimensional. It radiates sound in all directions, and the nature of the sound is not identical in all of those directions. For example, the sound radiating to the side of the loudspeaker is not the same as to the front. That has implications for how stereo images are formed, how the loudspeaker sounds when placed near walls, and how rooms influence the sound. Some simple physics will illustrate why that happens and lead to design approaches that ameliorate the problems.

Consider a simple cone drive unit in a box, which reproduces sound at various frequencies. At low frequencies, in which the wavelength is large compared with the cone dimensions, the radiated sound spreads uniformly around the loudspeaker. The level is the same in all directions. As the frequency is increased and the wavelength gets smaller, the sound starts to concentrate in the forward direction at the expense of the amount spreading to the side and rear. The sound essentially becomes focused, just like the beam of a flashlight compared with the light from a bare bulb. The bare bulb lights the room much more evenly than the flashlight. That effect is related to the size of the loudspeaker cone. A bigger cone means the beaming becomes significant at a lower frequency.

If such a simple loudspeaker is adjusted to have a relatively flat response on-axis (the forward direction), it will sound somewhat dull when listening off-axis because of the loss of the higher frequencies (see Fig. 1). Most quality loudspeakers are not as simple as this example. They consist typically of at least a woofer and a tweeter. That arises from the wide frequency range that must be reproduced and the requirements for adequately doing so. To reproduce loud bass sounds, a lot of air must be moved, albeit slowly. As a result, the woofer has to be large and heavy. Reproducing high frequencies does not require the movement of such a large quantity of air, but it does need to be moved fast. Accordingly, the tweeter is small and light.

It is the different physical size that is important. Size does matter when considering the focusing of the sound. The woofer will start to focus at a much lower frequency than the tweeter (see Fig. 2). When the two drivers are combined with a dividing network, the aim is to get as flat a response as possible over the whole frequency range. The question is, in what direction?

Traditionally, the design axis is directly in front of the loudspeaker. That means the response cannot be flat in other directions. The sound starts to lose energy as the frequency increases, up to the point where it crosses over to the tweeter. There the sound level jumps back up — because the tweeter is still relatively nondirectional at that frequency — before it starts to lose energy at some higher frequency. The dip in the off-axis output falls right in the most critical region of the hearing sensitivity of listeners.

Another consequence of splitting the frequency range between two or more drivers is brought about from their physical separation. Both drivers are active in the frequency range in which the sound transitions from the woofer to the tweeter. In that range, the on-axis sound from each driver can be added together beneficially. However, when you move off-axis to a location where you are no longer equidistant to each driver, you get destructive interference, resulting in peaks and dips in the combined frequency response (see Fig. 3). That is typically in the vertical direction for most loudspeaker configurations.

The nature of sound radiation from a driver and the need to split the frequency spectrum across two or more drivers results in a response that is not uniform in all directions. What effect does that have upon the sound of real loudspeakers in real rooms, and would any of that matter if you listened to a loudspeaker in a room devoid of reflections or outside?


If you listen to a loudspeaker outside, then all that matters is the on-axis sound, because the sound that radiates in other directions is lost, right?

It would be if you listened to one speaker in mono, but that's not really a popular option in these days of multichannel sound. When you consider just stereo, the world becomes much more complicated. In stereo listening, you perceive sounds that come not only from each of the two loudspeakers but also from phantom images that hang in space between the loudspeakers. The apparent position of those images depends upon the relative level and phase of the signals fed to the two loudspeakers. Their accuracy, stability, and quality depend on the two loudspeakers having identical frequency responses.

For example, consider a violin that is balanced to be positioned at the center of the soundstage. The sound of the violin consists of the fundamental and harmonics occupying a wide frequency span. If the two loudspeakers do not have identical frequency responses, the relative level between the two speakers will not be the same for the fundamental as for the harmonics, resulting in each appearing to come from a different position between the loudspeakers. The violin's image is now fat and bloated. Additionally, as notes are played, the violin's sound may seem to wander across the soundstage.

What does that have to do with the directional qualities of the loudspeaker? Fig. 4 shows that for a centrally seated listener, the angle subtended to each loudspeaker is identical. Assuming that they are symmetrical, the response from each loudspeaker is identical, though not necessarily the same as the on-axis response. However, for an off-center position, such as No. 2 or No. 3, the listener is now at a different angle to each of the two loudspeakers (on-axis to one and off-axis to the other). They now have different responses, and the image quality is degraded. Additionally, the tonal quality of the sound will be different from the two speakers, so a sound that pans from left to right will change its character as it traverses.


Once you move indoors, you have a whole extra set of problems to deal with. Do you ever listen to the sound of your voice or of other people in a room and note how different they sound? Because of its highly reverberant characteristics, a church is an extreme example of how a room can alter sounds. There a voice becomes rather indistinct, overwhelmed by the reverberation, and it is difficult to locate just where it's coming from. It also sounds louder than it did outside. That's because a considerable amount of the sound that had been directed away from you outside has returned, though much of it is highly delayed and perhaps modified because of absorption from furnishings. A home is rarely that reverberant; usually, it falls somewhere between the extremes.

When you listen to a loudspeaker in the room, you hear both the direct sound (the on-axis sound that comes straight at you) and the indirect sound from the reflections (the sum of the off-axis sounds). Listeners can generally differentiate between direct first arrival sound and the later reflections (and even the direction of these reflections), but those elements contribute to the perception of the sound balance of the loudspeaker in the room. Yet those off-axis sounds do not have flat response. As you move from room to room and change the ratio between direct and indirect sound, you will perceive a difference in the loudspeaker's apparent tonal balance.

Even changing the distance between the loudspeaker and listener will alter the sound balance. The farther away you are, the more the reverberant sound dominates and vice versa.

That makes life difficult for the loudspeaker designer, who has no control over where the loudspeaker is used. If you knew that the loudspeaker was to be installed in an indoor poolroom, you could limit yourself to designing for a relatively flat power response, because that would produce the smoothest sound balance in such reverberant surroundings. For a small, heavily furnished lounge, you could perhaps concentrate more on the direct sound. During the install process, extra EQ could be used to try to tailor the sound to the environment. That would still be a compromise, however. You need to reengineer the loudspeaker to minimize the nonuniform directivity, which will solve all of your problems — almost.


Nonuniform directivity is the enemy, so uniform directivity would seem to be eliminate any problems. But how directional? Should you have a nondirectional response at all frequencies, known as omnidirectionality?

Although an intriguing concept and one that has been attempted with limited success on numerous occasions, omnidirectionality has boundaries. Besides the great difficulty of engineering such a concept, the very desirability of such behavior can be questioned. An omnidirectional loudspeaker minimizes the direct to indirect sound ratio in the room, leaving the sound quality at the mercy of the room. Stereo imaging is likely to be vague, though big (for reasons beyond the scope of this article). Speech intelligibility is likely to suffer, similar to the church example.

A highly directional loudspeaker creates problems such as actually engineering such a concept, but a directional speaker certainly has some merit. A highly directional loudspeaker used in a church can significantly reduce the level of the reverberant sound and achieve great clarity but only, by definition, for a small listening area. That brings you back to the stereo sweet spot.

As usual, you are left with a compromise: a partially directional loudspeaker but one that attempts to maintain the directivity at all frequencies. That is called a controlled directivity loudspeaker. You cannot perfectly achieve that goal, but at least you can come close.

Conventional loudspeakers consist of several spaced drivers, each with differing directivities, giving rise to nonuniform off-axis responses, mutual interference effects, and subsequent imaging, sound balance, and room interaction problems. You simply have to match the directivities and move the drivers as close together as possible.


The key to matching the directivities is in understanding the mechanism that produces the directional response in the first place. A simple cone drive unit boosts its directivity with increasing frequency. The basis for that behavior can be found in any standard acoustics textbook, and it is governed by the mathematical and physical behavior of a piston radiator. For your purposes, it describes a rigid surface of given area moving backward and forward to produce sound. The key is rigid. That means the whole surface moves as one at all frequencies, an oft stated requirement of the perfect loudspeaker cone. Indeed, speakers have cones because they are more rigid than flat sheets. No practical material exists for a speaker cone that is perfectly rigid over a sufficiently wide band, though pure beryllium comes the closest. Most cones lose their rigidity by 1 kHz.

But what if the cone were designed to reduce in area with increasing frequency? Wouldn't that maintain a constant directivity? If you examine the vibration behavior of most loudspeaker cones, you'll find that they do shrink in radiating area with increasing frequency. The outer parts of the cone essentially stop radiating at the higher frequencies, leaving only the center (the part most closely connected to the voice coil) to do the work. But you also know from measurement that the driver still has a directivity that increases with frequency. What factor is missing?

Think of the acoustic megaphone that effectively amplified the sound of the voice and projected it great distances. That worked by guiding the wave as it progressed away from the mouth, better matching it to the air. It was also highly directional. If you were not in front of it, you heard very little.

The basic shape was that of a cone. The outer section of the loudspeaker cone that is not moving at high frequencies acts as a horn to the section that is, thus guiding the wave and restricting its directivity. So what you gain on the one hand you lose on the other, but it gives people a clue as to how to match the directivities. If you put a matching horn around the tweeter, you can make it guide the wave in a similar manner and impose the same directivity upon the tweeter as upon the woofer. By playing around with the shape of the wave guide (the preferred name for the horn), you can adjust the directivity versus frequency. Although you cannot achieve constant directivity at all frequencies, at least you can make a fair approximation over a good part of the spectrum.

A slight downside of that approach is that the wave guide's physical dimensions (essentially similar in size to the woofer cone) mean the tweeter must be located farther away from the woofer, exacerbating the interference problem. That goes against the stated objectives of improving directivity, but what else can be done?

When you think about separation of the drivers and its effect on the interference, you're not so much concerned about the actual physical distance but about the distance in wavelengths at the frequency at which the sound transitions from woofer to tweeter (the crossover frequency). The lower the crossover frequency, the longer the wavelength and the less effect a given physical separation will have. The solution is then simply to lower the crossover frequency to compensate. Because it can't handle the extra frequencies, a regular tweeter won't cut it. However, the other benefit of the wave guide — that of the improved match to the air — now works in your favor. The improved efficiency can be traded for bandwidth, and the problem is solved. Yet you can do better.


The drivers are still separated, but the optimum solution would be no separation at all. That is called concentric, in which a tweeter is positioned within the woofer, mounted at the apex of the cone and coaxial to it, ideally. No separation means no interference. Furthermore, because you modeled the shape of the tweeter wave guide on the shape of the woofer cone, the cone itself now acts as the perfect wave guide and results in near identical directivities.

The fundamental idea is not so new. In fact, Tannoy championed a similar approach many years ago, but practical, low-cost solutions had to wait for technology to catch up, primarily with the ready availability of neodymium magnets. KEF Electronics was the first company to popularize the concept with the Uni-q drivers, but there are many examples of the approach, including SEAS, Thiel, and Pioneer. The directivity at the crossover frequency is matched for more than 100 degrees around the loudspeaker. When measuring good examples of the concentric drivers, it is almost impossible to establish where the crossover frequency is set just by measuring the off-axis response.

As with any technology, there are different levels of refinement. The best examples, though not yet possessing absolutely constant directivity, do have smooth response both on- and off-axis and lead to consistent sound in a variety of rooms and locations. Newer materials for the cones, by allowing for more freedom in choice of cone shape, are already starting to show promise for even better directivity performance. The future looks good for concentric technology.

Andrew Jones studied physics at Surrey University in England before joining the audio research group at Essex University to work on computer modeling of loudspeaker crossover networks and active noise control. He has worked as chief engineer for KEF Electronics Ltd. and Infinity Systems Inc. He is currently manager of R&D of speaker systems for Pioneer Electronics.