Point Sources: Spherical Spreading, Near- and Far-Field Designations
Figure 18.1a shows an ideal point source that, as a function of distance, experiences a rapid increase in the surface area over which the sound energy is distributed. Because the energy per unit area (sound intensity) is inversely proportional to the square of the distance from the source, this phenomenon has come to be called the inverse-square law. The sound level correspondingly falls rapidly, at a rate of -6 dB/dd (dd = double-distance). This happens only in the far field of the source.
Beranek (1986) suggests that the far field begins at a distance of 3 to 10 times the largest dimension of the sound source. At this distance, the source is small compared to the distance, and a second criterion is normally satisfied: distance2 = wavelength2/36
In the near field, as shown in Figure 18.1b, the sound level at any frequency is uncertain. Figure 18.1c shows estimated distances at which far-field conditions should prevail for a loudspeaker system and for its components. This would be the minimum distance at which a microphone should be placed for measurements and at which listeners should sit to have a predictable experience.
In a room, closely adjacent reflecting surfaces must be considered to be part of the source. This means that the far field for the combination (loudspeaker plus a very early reflection) can be very far away.
Diffusers behave as secondary sources of sound, and they can cover significant areas of room surfaces. Cox and D'Antonio (2004, p. 37) point out that listeners should be placed as far from scattering surfaces as possible, at least three wavelengths away. For devices that are effective to 300–500 Hz, this is a minimum distance of about 10 ft (3 m). As they realistically point out, "In some situations, this distance may have to be compromised."
So what is heard while standing close to the loudspeaker and its immediate environs can be very different from what is heard farther away, especially if one is moving around and by doing so enhancing the audibility of any near-field lobing or acoustical interference. Such effects are especially audible with stable broadband sounds like pink noise. Back in the listening area, sitting down, listening to music or movies, the audible result will be very different and much more pleasant.
FIGURE 18.1 (a) The classic illustration of spherical spreading, originating with a point source. In the far field, the sound level falls at a rate of -6 dB per double-distance. (b) A graphic illustration showing the disorderly near field and the predictable far field behavior of a source. (c) Estimates of the distances at which far-field conditions are established for a three-way loudspeaker system and for its components, singly and in combination.
In recording control rooms, it is common to place small loudspeakers on the meter bridge at the rear of the recording console. These are called near-field or close-field monitors because they are not far from the listeners. As shown in Figure 18.1c, the near field of a small two-way loudspeaker (the midrange and tweeter of the example system) extends to somewhere in the range 21 in. to almost 6 ft (0.53 to 1.8 m). Including the reflection from the console under the loudspeaker greatly extends that distance.
There is no doubt, then, that the recording engineer is listening in the acoustical near field, and that what is heard will depend on where the ears are located in distance, as well as laterally and in height. The propagating wavefront has not stabilized, and as a result this is not a desirable sound field in which to do precision listening, but as they say, perhaps it is "good enough for rock-and-roll."
Some of these far-field distances are much greater than the 1 m distance universally used for specifying loudspeaker sensitivity (e.g., 89 dB @ 2.83 v @ 1 m). There is no problem here because in the standards that specify the rituals of loudspeaker measurements, it is stated that the measurement should be made in the far field, whatever that may be, and then the sound level that would be expected from a point source at 1 m should be calculated.
For example, if a measurement is made at 2 m, 6 dB should be added to arrive at the sound level at the reference distance, even though 1 m may be within the near field of that particular loudspeaker. The 1 m standard distance is therefore a convenience, not a directive that a microphone should be placed at that distance. Many people have misunderstood the intent of the standard distance, including some major players in the loudspeaker business.
If it is necessary to make measurements within the near field, useful data can still be obtained by spatial averaging: making several measurements at the same distance but at several different angular orientations with respect to the loudspeaker and averaging them. This is another of those uncertainty principle situations. By spatial averaging we have a better idea of the true frequency response, but we don't know the axis to which it applies. If we measure at a single point within the near field, we know the axis precisely, but we don't have a good measure of the frequency response.