The Importance of Speaker Directivity (Sept 1979)

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by Dan Queen

Phase, time-delay, coherence, dispersion--these have been some of the watchwords in loudspeaker de bates over the past few years. The "omnidirectional versus directional" argument is also gaining a place with the "tubes versus transistors" and "triodes versus pentodes" controversies of years back.

All these arguments reflect upon our knowledge of how we hear music and on what things in the sound wave produced at the recording site are important enough to be reproduced accurately in the listening room.

Seldom in such discussions are those two very important factors--the recording site and the listening room--brought into an evaluation of the merits of a loudspeaker design.

Yet, it may be the interaction of the loudspeaker with characteristics of the two rooms, particularly those of the listening room, that have more to do with the sound quality of a given loudspeaker than any traditional measurements.

There are many ways to describe the rooms in which music may respectively be recorded and reproduced: The dimensions of the rooms may be stated; the shapes of the rooms may be stated or the materials of which they are constructed may be described. Important to acousticians are the sound fields which build up in the rooms.

These sound fields are described in terms of an interaction of room acoustics and characteristics of human hearing (or psychoacoustics).

When a sound source in a room emits a sound, it will first travel directly from the source to the listener.

However, the sound will also travel in other directions, striking walls, and ultimately reflecting back to the listener. There is obviously a shorter time required for a sound to travel directly to the listener from the loudspeaker than via a reflection to the listener, and these differences in time are small enough to be measured in milliseconds.

Sound travels about three tenths of a meter (or about one foot) every millisecond. Because our hearing sense has evolved in bounded areas, such as caves and dense forests, it is natural that we would have developed some means of using the sense for discriminating between direct sound and its reflections. This discrimination, in fact, gives us much of our ability to determine the direction from which a source has come, that is, our ability to localize a sound.

above: In systems where two drivers cover the same tones, cancellations can cause different perceived locations for fundamentals and overtones.

Part of this ability depends on some of these reflections fusing themselves with the direct sound. A voice sounds louder in a room at a distance of a few feet than it does outside at the same distance. Reflections have added loudness to the sound which reaches us. However, this ability of the ear to "add" the reflections to the direct sound is limited by time, so after a few tens of milliseconds, later arriving sounds no longer fuse with the direct sound but begin to be heard as echoes or, when there are many such late reflections, as reverberation. Thus, acousticians define three fields in a room. The first is the direct sound; the second, the early reflections, and the third, the late sound or reverberation.

Home listening rooms seldom sound reverberant. The majority of the sound goes into the direct sound and early reflections. In fact, early reflections predominate in a home listening room. On the other hand, in a concert hall or large studio, there is generally considerable reverberation and relatively few early reflections.

This is because sound has to travel so much greater distances to reach reflecting surfaces and return to the listener. By the time it does return to the listener, most of it will be in the category of late sound.

Distance is the key. Because of the distances involved, it is very difficult to make a home listening room sound anything like a concert hall. To pro duce concert-hall sound, it is necessary that some late sound be on the recording. Nevertheless, use of time-delay circuitry and logic to try to favor the late sound, delay it, and radiate it into the room from directions other than the front, can be effective in simulating the concert hall in the room.

However, in doing so, it is necessary that the loudspeaker used does not introduce some distortion of the natural sound fields because of peculiarities in its own characteristics. And those loudspeaker characteristics most important to the placement of sound in the listening room are the directivity characteristics.

Experimenters in the field of psychoacoustics have found that the hearing mechanism can be fooled, using two sound sources, such as stereo headphones, into thinking that a sound source is actually between the headphones. They find that we are fooled into thinking the source is centered when the signals are identical. As one signal becomes softer than the other, the sound seems to move toward the louder earphone. Also, if one sound is delayed relative to the other, the sound seems to move toward the un-delayed earphone.

Using earphones in this manner, a delay of only one millisecond will make equal amplitude sounds appear to be entirely at one side of the head.

However, this phenomenon appears to hold true mainly when most of the sound is at low frequencies. When the sound is at high frequencies, the intensity cue seems to be most import ant. Remarkably, under the artificial conditions set up by earphones and synthesized signals, one can even pro duce two images, one controlled by the intensity and the other by the time delay.

Fortunately, when one places two loudspeakers in a room at the usual locations for stereo reproduction, both ears are receiving signals from both loudspeakers with very small time differences at the two ears. Nevertheless, the amplitude differences continue to appear. An amplitude difference of 10 decibels seems sufficient to shift the sound completely to the louder loudspeaker (10 decibels represents a doubling of perceived "loudness").

This means that amplitude differences of less than 10 dB tend to cause a sound to be located between the loudspeakers. This, of course, is the basis of stereophonic imaging. But, when one places the loudspeakers in a room, such as a residential living room, there can be more than one thousand reflections from room surfaces that are within 10 dB in level of the sound coming directly from the loudspeaker.

How, then, is it possible to obtain a stereophonic image in a real room? One apparent answer is that each of the reflections acts, in effect, like another loudspeaker, and each of the new reflection-speakers has the same relationship to the original loudspeaker as each of the new reflection-speakers has with any other. To make things clearer, let's look at a diagram in which we see a sound moving directly to a listener and another reaching the listener via a wall reflection. The listener places the source at a point between the loudspeaker and the reflection, but, because the loudspeaker should be louder, closer to the loudspeaker.

Each subsequent reflection will itself again shift the image in one direction or another--eventually averaging out in a final position. If a loudspeaker produces a lot of reflections from a wall to the side of it, it is very possible that the perceived direction will be closer to that wall than to the loudspeaker. Thus, it is possible for a pair of stereo loudspeakers to produce an image which is wider than the actual distance between the loudspeakers.

But all is not as well as it seems. The hypothetical loudspeaker we have been describing may well emit sound as efficiently in the direction of the wall as in the direction of the listener.

In reality, most loudspeakers have out puts which vary with direction.

above: The human ear, unlike a sound level meter, can easily detect subtle differences between steady-state and pulsating tones.

It can be argued that if the loudspeaker projects most of its sound toward the listener and much less toward the walls, a better stereo image should be obtained. This would probably be true if it were physically possible to produce a loudspeaker that has the same directional pattern at all frequencies. When the directional pat tern varies with frequency, one could easily find the fundamental of a musical instrument appearing to come from one direction while its overtones come from another direction.

The radiation patterns of two drivers show us why this is so. If you drop one pebble in a pool of water, waves will radiate smoothly out in all directions from the point of impact. However, if you drop two pebbles, the two sets of waves will interact. In some directions, the waves will add on top of one another, while in other directions, the wave from one stone will tend to cancel the wave from the other stone.

Where the cancellation and addition actually take place depends on the distance between the crests of the wave.

For waves of sound in air, the distance between the crests determines the frequency of the sound. Thus, the waves of the overtones from an instrument, being higher in frequency, will have different cancellation patterns than the waves of the fundamental.

A listener may find himself sitting at a point where, at the fundamental, the waves coming direct to him from the loudspeaker are adding, while the waves heading toward the wall or reflecting surfaces are cancelling. The fundamental will then appear to come directly from the loudspeaker. On the other hand, at the first overtone, the situation can easily reverse itself, moving the overtone in the direction of the reflective surface.

The result is the hazy, unclear sound which is characteristic of many loudspeaker systems. It is sometimes mistakenly called poor transient response, which is not true in the pure electrical sense, although it may be considered so in terms of spatial acoustics. In any case, it is not a problem which will make itself known by the measurement of tone bursts in an anechoic chamber.

The property of the ear which enables it to average the direction of a sound from its origin and its reflections operates only in the first tens of milliseconds after the direct sound.

Furthermore, in actual listening rooms of the sizes found in residences, most of the reflections which are within 10 dB of the level of the original sound, occur in the first 10 milliseconds or so.

While the exact time at which the ear is no longer able to fuse the reflections and begins hearing them as echoes and reverberation seems to vary due to many factors, it is generally agreed that it happens at a time greater than 20 milliseconds and shorter than 100 milliseconds.

This means that problems due to loudspeaker directivity which occur in the home listening room may not occur in a large hall--where very few reflections arrive at the listener during the time immediately after the direct sound. On the contrary, most of the reflections in the large hall are heard as echoes and reverberation. This is why a loudspeaker that sounds excellent in a large hall may be virtually unlistenable in a small room--and vice versa.

Furthermore, before any discussion of the relative merits of directional versus omnidirectional loudspeakers can take place, one must consider whether or not the speakers are truly directional or truly omnidirectional.

We have seen wave interference as illustrated by dropping two stones in a pool of water.

above: To a listener, the "sound" of a speaker is a combination of the direct and reflected sound.

In loudspeaker systems, the two-stone analogy applies in the crossover region of the loudspeakers as well as in loudspeaker systems which have more than one source radiating the same frequencies.

Nevertheless, even when only one driver is radiating the same frequencies, similar interference occurs. It can be illustrated by dropping a straight rod into that same pool of water. Even if that rod is dropped parallel to the water surface, the wave front started from one end will tend to interfere with the wave front from the other end.

In fact, the only way that one can get the smooth, circular "omnidirectional" ripples is to use a single very small pebble. This, moreover, is true with sound waves. A perfect omni-directional pattern can be obtained only with an infinitely small source--or, at least, one that is very small compared to the smallest wave one wishes to produce.

However, the smaller the pebble, the smaller the size of the waves that can be produced. The same is true in generating sound waves. While one would like a small "pebble" to pro duce uniform response, one needs the larger "rod" to produce sufficient sound power. The task in loudspeaker design is to solve this dilemma. Merely placing loudspeakers around a cabinet does not produce true omni-directionality. It is like dropping pebbles in a circle. The wave interference is still there and is still strong.

A possible solution is illustrated by dropping the rod vertically into the water. One can make the waves go out evenly around the rod--but if there were, in effect, a "vertical water" there would still be wave interference. Nevertheless, it is possible, using devices such as "radial horns"--which are horns that open in a circle--and some types of electrostatic full cylinders, to obtain a relatively uniform omnidirectional pattern, that is one nearly perfect in the horizontal plane.

In rooms of the size of residential listening rooms, it makes some difference if one achieves uniform directionality in a directional speaker or an omnidirectional speaker. The omni directional speaker will have to be more efficient because it will be radiating towards all surfaces, which means that it may be subject to "absorption" in some surfaces more than a directional radiator will be.

However, at present, it is not possible to make a directional radiator which has a uniform pattern with frequency.

Reflected sound acts like a ball bouncing off the cushions of a billiard table. If the cushions are springy, the ball loses only a little energy each time it hits. However, as the cushions be come old, they start to "absorb" a good deal of energy from the ball each time it hits. In the room, hard plaster walls absorb little, while carpets, drapes, upholstery, acoustic tile, and people absorb more. But the absorption varies with frequency, aggravating the effects of uneven loudspeaker directivity.

above: A system with 360-degree horizontal dispersion would have no shifting images due to cancellation effects.

Uneven absorption could also create problems with a "perfect" directional speaker, since some of its sound output will produce reflections which eventually get to the listener. Because the directional loudspeaker favors only the surfaces in front of it, rather than all the variegated surfaces of the room, it cannot average out the room differences as well as an omnidirectional speaker. In contrast, the sound of a truly omnidirectional speaker will hardly vary as one moves about the listening room.

Furthermore, the ability of the omnidirectional speaker to even out room differences allows the effective use of equalizers to smooth the response of the speaker-room combination. Thus, ideally, the combination of a loudspeaker that directs its sound only to listener locations, with a room which reflects all frequencies equally from all directions, should provide the most realistic sound. Unfortunately, such a loudspeaker is not technically feasible, and such a room would have to exclude furniture, decor, and--most significantly--people, making the omnidirectional speaker the better choice from the directivity standpoint.

( Audio magazine, Sept. 1979)

Also see:

Influence of Listening Rooms On Loudspeaker Systems by Roy F. Allison (Aug. 1979)

QUICK BUILD--Build A Speaker Impedance Checker (Aug. 1979)

Tape-to-Deck MATCHING For Best Dolby Tracking (Sept. 1979)

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