44  How Loudspeakers Work

Figure 2.14: Much-reduced response disturbances due to corners, added to 6 dB rise; Olson optimal loudspeaker enclosure; dimensions given in text (after Olson, 1969).

2 feet and 3 feet. The drive unit was mounted midway between two long edges and 1 foot from the top short edge.

Using the information derived from these enclosure shapes, Olson suggested an enclosure that would give good results while still fitting into a domestic setting rather better than a sphere. The results are given in Figure 2.14, and the response deviations are about 2 dB; not as good as the sphere, but far better than the simple rectangular box. Olson says about its dimensions:

A rectangular truncated pyramid is mounted upon a rectangular parallelepiped. The lengths of the edges of the rectangular parallelepiped are 1, 2, and 3 ft. The lengths of the edges of the truncated surface are 1 ft. and 2½ ft. The height of the truncated pyramid is 6 in. One surface of the pyramid and one surface of the parallelepiped lie in the same plane.

There are a few interesting points about the Olson tests which are not normally quoted. First, the drive unit he used was specially designed and had a cone diameter of only 7/8 of an inch, so it was small compared with the wavelengths in question and could be treated as a perfect piston; that is why it looks so tiny on the enclosure sketches. All the measurements were done on-axis in an anechoic chamber.

Second, while the reference that is always given is the 1969 JAES paper, because it is accessible, the original paper was presented at the SecondAnnual Convention of theAES in 1950. This accounts for the somewhat steampunk look of the measuring equipment pictured in the paper.

Other workers in this field have reported that further reduction in the response ripples can be obtained by optimising the driver position and rounding the enclosure edges.

Sound Absorption in Air

The further you are from a source of sound, the lower the SPL you experience, as the energy has spread out more; this is sometimes called “geometric spreading”. However, there is another form of attenuation that increases with distance—part of the sound is absorbed as it is conducted through

How Loudspeakers Work  45

the air. Some of the acoustic energy is converted to heat by viscosity effects in the air itself and by vibration of water molecules mixed with the air; the attenuation therefore increases with rate of movement and so with frequency. It is also affected by the air temperature and pressure, but primarily by frequency and the relative humidity. Figure 2.15 shows the effects; virtually nothing happens below

2 kHz, but the attenuation increases quickly up to 10 kHz. The exact attenuation can be calculated, but it is a formidable equation; [33] it is said to be valid for an air temperature of less than 57°C, a pressure under 2 atmospheres, and altitudes up to 3 km. I hope that will cover most open-air concerts.

Since the amount of attenuation depends on the distance the sound travels and is negligible for short distances, this is nothing to do with hi-fi, and in PAwork is normally only a significant issue for large outdoor performances.Arule of thumb I have heard more than once is: “If at 100 feet the effects are audible, at 500 feet they are likely to be serious.”

From Figure 2.15, if the humidity is 40%, 2kHz will only be attenuated by 0.3 dB at 100 feet, but 10kHz is down by 4.5 dB. The decibel losses are linear with distance, so at 200 feet 2kHz suffers 0.6 dB loss, but 10 kHz is now down by a rather serious 9.0 dB. Moving out to 500 feet gives us

1.5 dB loss at 2 kHz and a 22.5 dB loss at 10 kHz, which I would agree is “serious”. Generally you are unlikely to encounter humidity outside of the range 30–80%.

Figure 2.16 shows the data replotted to give a better idea of how the high frequencies are attenuated; up to 10 kHz and down to 30% humidity the slope is no greater than 6 dB/octave, and the roll-off can be compensated with simple 1st-order equalisers.

Because the attenuation increases with distance, there are limits to what can be done with overall HF equalisation.Applying 22 dB of boost at 10 kHz is not practical—it might sound good at 500 feet but would give horrible results at 100 feet. There are at least two answers to this problem—the first is the

Figure 2.15: Attenuation by air absorption increases with frequency and decreases with humidity. Results for 30m (approximately 100 feet).

46  How Loudspeakers Work

Figure 2.16: Attenuation by air absorption plotted to show the roll-off with frequency. Results for 30 m (approximately 100 feet). The straight line is at −6 dB/octave.

reintroduction of delay towers to shorten the air path to the listener, but nobody really wants to do that because of the extra hardware, cabling, security, and so on. A much better solution is to exploit the useful property of vertical line arrays so that they maintain a −3 dB loss per doubling of distance for much further at high frequencies than at low frequencies.

Modulation Distortion

With any crossover the drive units have to handle a range of frequencies, and this leads to the problem known as modulation distortion. What has been called “total modulation distortion” [34] is made

up of two components: amplitude modulation distortion and frequency modulation distortion. Both