[SoundStage!]Getting Technical
Back-Issue Article

February 2005

Understanding "Sound Power" with Ian Colquhoun of Axiom Audio

An audiophile has cause to blush if he’s never heard of Canadian physicist Dr. Floyd Toole. It was Toole’s groundbreaking research for the Canadian-government-sponsored National Research Council (NRC) that led to the development of the measurement techniques used today by loudspeaker designers worldwide. Toole stressed the importance of the frequency-response graph as an indicator of loudspeaker performance, and even his critics have to admit that the graph does correlate with listeners’ preferences. Of course, any time objective metrics -- particularly numerical values -- are used to describe subjective experience, detractors voice their opinions too.

Some criticized Toole’s use of the NRC’s infamous anechoic chamber. Padded with sound-absorbent material, the chamber’s design prevented any sound waves from bouncing off surfaces, which allowed Toole and others to measure the sound from the loudspeaker without any contamination from reflected sound. The critics’ complaint was simple: "If loudspeaker ‘A’ produced a flat frequency response in this artificial environment, how can you claim it will perform the same in a user's environment?"

This is a valid point. Measuring direct sound is only one component of the sound that reaches our ears. Early reflections -- the sound waves that bounce off only one surface before reaching the ear -- and reverberant sound -- the rest -- are the other two components of the sound we hear in a real room. With the anechoic chamber absorbing sound waves and thus eliminating the reflections and reverberant sound, how useful were Toole’s measurements in an anechoic chamber for predicting at-home performance? Allan Devantier’s 2002 paper, "Characterizing the Amplitude Response of Loudspeaker Systems," presented at the annual convention of the Audio Engineering Society, asked just this question. Devantier measured the performance of a loudspeaker in 15 different domestic environments, and his results proved that Toole’s measurement of frequency response in an anechoic chamber is still a reliable indicator of performance.

But Toole worked with other measurements beyond straightforward frequency-response charts as well, including one possibly more useful because it measures the response of the speaker over 360 degrees. This metric -- called "total radiated sound power," or sometimes just "sound power" -- is defined as follows: "Total sound power is used to represent the sounds that arrive at the listener’s ears after encountering more than one room boundary. The total sound power is the weighted average of all frequency-response measurements." It is this averaging of all frequency responses that enables sound power to be a realistic laboratory-based predictor of a loudspeaker’s real-life performance in a non-laboratory environment.

Sound power is measured in watts, and when referenced to a standard value of 10 to the negative power of 12, can be expressed in decibels (dBs). Typically, frequency-response graphs measure on-axis and some off-axis responses of a loudspeaker at discrete intervals. Sound power, however, is a measurement that captures the total amount of sound radiating from every direction out of a loudspeaker. This is an important consideration in a home environment, because in a normal listening environment -- unlike in an anechoic chamber, where it’s absorbed -- sound bounces off walls, ceilings, and furniture before eventually reaching the listener’s ears.

NRC personnel measure total radiated sound power by measuring the speaker’s on-axis response first, and then they turn the speaker by 15-degree increments and take a measurement at each interval until they’ve gone all around the speaker. The speaker is then placed on its side and the speaker is measured all around again in 15-degree increments. That measures the acoustic output of the speaker, horizontally and vertically, over 360 degrees. The computer then takes all those measurements, calculates an average, and produces the "total radiated sound power" chart. With those measurements, the "directivity index" can be calculated (see sidebar), as well as others because a lot of data has been gathered.

The "Directivity Index"

When the measurements for the "total radiated sound power" curve are taken, other measurements are possible to calculate, too. One of those is the directivity index, or DI for short.

I asked the experts at NRC for their definition of the directivity index and they said this: The directivity index is "a measure in decibels of the difference between the sound power radiated by an imaginary, perfectly omnidirectional loudspeaker having a frequency response equal to the on-axis response of the test loudspeaker, and the sound power actually radiated by the test loudspeaker. In other words, a directivity index of zero indicates the test loudspeaker is perfectly omnidirectional. An increasing directivity index indicates a progressive concentration of the sound output in the direction of the reference axis."

Andrew Welker, the lead designer of Mirage’s omnidirectional speakers, likes to use the directivity index when designing his speakers. Mirage places a strong emphasis on dispersion, with unique speaker designs that disperse sound more effectively than conventional designs. We’ve reviewed a number of his "OmniGuide"-equipped speakers on SoundStage! Network sites and were impressed. Alison interviewed Welker about his speakers, an article that was published in February of last year. He had this to say in that interview: "The directivity index (DI) is calculated from the same series of curves used to produce the sound-power curve and gives us a representation of how a loudspeaker's dispersion varies with frequency. The DI of a loudspeaker using the OmniGuide will be very close to the theoretical ideal: a flat line with very little variation with frequency, suggesting wide dispersion at all frequencies."

If you look at the sound-power curve of Axiom’s M3ti loudspeaker, you’ll see that the directivity index is plotted on the same chart. The directivity index is rather simple to read because it correlates with the sound-power measurement. In the bass region the directivity index is essentially zero -- this is because bass frequencies tend to be non-directional, even in front-firing speakers, making the speaker omnidirectional in that region. Higher frequencies, however, are more directional. You can see that as frequency increases, so too does the directivity index. The M3ti is most directional in the highest frequencies, which is no surprise. From the bass to the higher frequencies, though, the directivity index rises fairly smoothly, indicating well-controlled dispersion characteristics as frequency increases, which is what designers such as Colquhoun strive for.

...Doug Schneider

One of the loudspeaker designers who worked with Toole at the NRC is Ian Colquhoun. A member of the original group of researchers involved in developing psycho-acoustical testing protocols at the NRC and the founder of Axiom Audio, Colquhoun provided me with a real-life example of sound-power measurement using Axiom’s M3ti loudspeaker, which SoundStage! reviewed in December of 2000.

"The M3ti is one of those speakers that does many things well," Colquhoun explained, as he set up the demonstration. "For instance, it has excellent bass response for its size, which means it can be used in many applications without a subwoofer. It is linear and has good off-axis response for a 6 1/2" woofer. The M3ti also has the ability to play quite loud (high sound pressure level, or SPL) without introducing any distortion. That quality is particularly hard to find in a bookshelf speaker."

Colquhoun can perhaps be forgiven for promoting his own product -- he’s a believer in his wares. But, as he explained to me, he still considers himself to be an engineer first and businessperson second.

"I am the president and sole shareholder of Axiom, but my main focus is product engineering and loudspeaker design, which began back in 1980 when I joined the group headed by Dr. Floyd Toole. This research went on through the 1980s and early ‘90s, and resulted in the most extensive body of scientific work ever done on loudspeaker sound and how it related to user preferences."

The goal of that research was to demonstrate that loudspeaker design is a science, not a "black art," and that careful scientific measurements of loudspeaker performance can be predictors of listener preferences. The successful attainment of this goal was what spurred Colquhoun to begin building his own design laboratory at Axiom Audio in the 1990s, although he says he still uses the NRC’s facilities regularly.

"The sound-power graph is what I would call a ‘secondary’ graph in speaker design -- the reason being that you know what it is going to look like from the analysis of the main family of curves measured in the front hemisphere," says Colquhoun, explaining that the "family of curves" represents the on- and off-axis frequency responses of the speaker measured from in front of the speaker, and at increasing angles away from the position, both horizontally and vertically. The front hemisphere refers to the area in front of the speaker’s front baffle, from on-axis to 90 degrees off-axis, both vertically and horizontally. (The rear hemisphere would be the remaining area behind, and the sum of the front and rear hemispheres is what’s used to calculate total radiated sound power.)

"That group of curves is by far the most useful in predicting how the speaker will sound in double-blind listening tests," Colquohoun says.

Due to the directionality of frequencies, a good sound-power curve should start to fall off at 150Hz and drift downward, reaching about -10dB by 1.5kHz. From there, it will tend to remain reasonably linear at the -10dB mark.

"At one time, there was a camp of thinking (now long gone) that believed a proper speaker design would have a completely linear sound-power curve," says Colquhoun. "A speaker like this would obviously have a serious lack of bass, among other problems."

For traditional, front-firing loudspeakers, the sound-power curve will have its highest point in the bass region, due to the non-directional behavior of bass frequencies, and will likely be downward sloping, leveling off as Colquhoun says. It should also be "flat," just like a typical frequency-response measurement, meaning that no strange suckouts or emphases in any particular region will occur. When it’s flat it usually means that the individual response curves are quite similar and, as a desirable result, the reflective and reverberant soundfields (off-axis response) should sound similar to the direct sound (on-axis response).

Axiom Audio M3ti Loudspeakers

Frequency response on-axis (top line), as well as 15- and 30-degrees off-axis (middle and bottom lines)

Sound power (top line) and the directivity index (bottom line)

200502_soundpowergraph.gif (25399 bytes)

As Devantier concluded in his paper, "For a loudspeaker to perform well, direct sound, early reflections, and the reverberant sound must all be considered."

From all indications, then, the importance -- and validity -- of Toole’s pioneering NRC work have been verified. Devantier’s work seems to demonstrate conclusively not only that Toole’s frequency-response graph is still a reliable indicator, but perhaps more importantly that sound power is an even more robust predictor of loudspeaker performance. And Colquhoun’s successful speaker designs prove that speaker designing can be done with a firm understanding of science. While this conclusion may not be sufficient to silence the critics, it should be enough to allow Dr. Floyd Toole to take his rightful place among the great pioneers of audio research, and his work at the NRC is as valid today as when he published it in the ‘80s.

...Alison Aulph

To learn more about Axiom Audio, visit www.axiomaudio.com.


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