ALTHOUGH WE ARE ALL FAMILIAR WITH THE LOUDSPEAKER frequency response graphs and measurements that we see on manufacturers' spec sheets, such measurements do not really tell us how a particular loudspeaker is going to sound in a given environment, unless that happens to be an anechoic chamber — and how useful is that? However, there is a measure that can give us a much better idea of how the speaker will sound in a real-world installation, particularly within a reverberant space. The parameter is sound power (or Lw rather than Lp for those of you with a mathematical bent). Sound power can also indicate the potential intelligibility of a sound system to be gained.

SOUND POWER SPECIFICATION

So what is sound power and what can it do for us? Essentially, sound power describes the total radiated acoustic output of a loudspeaker. It is rather like taking a series of frequency responses around the loudspeaker and combining (integrating) them into a single measurement graph. The result is expressed as power in watts rather than pressure in pascals. By referencing this to a standard value, 10^-12 watts, we can obtain a measurement in decibels, in terms of Lw instead of the more usual decibels Lp, which has a reference value of 20 micropascals (20 × 10^-6 Pa).

Imagine a loudspeaker operating in a reflective or reverberant space. Normally, we are concerned with the sound that it radiates either on or just off axis in a forward direction (or, to put it non-technically, the bit we want to point at the audience). This is the sound that the normal axial frequency response describes, particularly if supported by some off-axis curves. What we tend to forget, however, is that loudspeakers also radiate in other directions. In fact, if freely suspended away from any boundaries, a loudspeaker will radiate all the way around.

In a reverberant or reflective space, this side and rear sound radiation will also reach the listener and will affect the spectral balance of what we hear. As can be imagined, this unwanted sound radiation is highly colored and will usually have a radically different spectral response to that generated and perceived on axis. Figure 1 illustrates the basic concept.

Interestingly, with most loudspeakers, there is usually a greater area of non-useful sound than useful sound. Only by integrating over the prescribed areas, and taking the relative radiation components into account, can this all be quantified: That quantification is the sound power specification. Therefore, a loudspeaker with an even or flat sound power characteristic would seem like a good one, in that the off-axis radiation would have a nominally similar characteristic to the on-axis sound (assuming that the loudspeaker has a flat axial frequency (Lp) response, which, after all, is the inherent aim of most loudspeakers). In other words, the reverberant sound component would have a similar response to the direct sound.

USING SOUND POWER DATA

Very few manufacturers provide sound power data. However, during a recent housecleaning, I came across a 1985 EV data sheet that did provide this information (see Figure 2).

This is a good power characteristic and fairly typical for such a device. More recently, JBL published power response data for its high-quality studio monitor loudspeakers. However, this is hardly typical of sound and voice-alarm systems, so I recently made my own measurements, as seen in some of the graphs below. (But first, my disclaimer: As my measurement technique developed, my data presentation technique also changed. Some care needs to be taken when reading these graphs; however, if you focus on the general shape of the curves, you'll get the idea.)

Figure 3 shows the power response for several speakers. The orange line shows power response for a 5-inch cone loudspeaker. This is typical for a device that either has a collapsing coverage angle or progressively gets more directional.

The point to note is the collapsing power response: There is a steep gradient from low to high frequencies. The pink line in the graph shows a typical power response for a CD horn. The device does not have really effective pattern control until around 1 kHz. And, as can be seen from the power response, from there on up, the acoustic power output is pretty constant as well, being within just 3 dB. Now look at the blue curve. This shows the power response of a short column loudspeaker with an HF crossover just above 2 kHz. Again, the collapsing response can be seen at the low to mid-range frequencies but is overcome at the high frequencies by the HF device.

By contrast, the purple charting in the figure shows the response for a typical ceiling speaker, measured in half space so as to more closely mimic its real performance when in use. The device exhibits a reasonably well-controlled characteristic up to around 2 kHz when the dispersion collapses in a fairly typical manner and the power output falls.

Figure 4 shows the power response for two distributed-mode loudspeaker devices. These bare out the theoretical prediction that such devices, when correctly designed, should exhibit a nominally flat power response.

An interesting power response is seen in the response for a 750mm column loudspeaker (Figure 5). This is typical for such a device with a well-pronounced, high-frequency roll-off in power output, but in this case with a 6dB peak at around 500 Hz as well. The normal, axial frequency response for the unit, however, is respectably flat and thus at odds with the sound power output.

I also looked at the power response for a compact directional sound projector. This, too, exhibited a peak at around 500 Hz but maintained a reasonably flat response up to 4 kHz before collapsing. On the other hand, the corresponding axial frequency response, although exhibiting a hint of the peak at 500 Hz, did not give any indication of the power response characteristic of the unit.

The response of the projector when measured in situ in a reverberant concourse is shown in Figure 6. You can see that the actual results are determined by the power response rather than the axial frequency response.

A similar trend was apparent in my in situ response measurement of the column loudspeaker shown in Figure 5, again indicating that it is the power response predominantly at work rather than the axial frequency response, with a combination of the two giving rise to resulting audible response.

Whereas the power response of a loudspeaker can readily be compensated for by appropriate equalization, such filtering will unavoidably affect the axial (direct) response, which makes system equalization when using such devices a painstaking and often frustrating process.

That the reflected and reverberant fields can dominate the system response yet still provide adequate intelligibility can come as a surprise. For example, in a 2-second space with a distributed sound system, the direct-to-reverberant ratio can be quite negative: -9 dB for a resultant intelligibility of 10% Alcons (0.52 STI) or -5 dB D/R for 5% Alcons (0.65 STI). The corresponding C50 may also be significantly negative under such circumstances.

CONCLUDING THOUGHTS

It is clear that, in reverberant or very reflective spaces, the loudspeaker's sound power response often dominates, even when observed using time-windowed responses. Subjectively, a combination of both the direct and reflected fields is heard; and in many cases when equalizing, a compromise has to be reached between the often conflicting requirements of these individual responses.

Loudspeakers that exhibit sound power responses radically different than their axial frequency responses generally do not equalize as easily as those devices that more nearly track each other and offer smooth or nominally flat power responses. Constant directivity horns and similar devices seem to provide this latter characteristic, as do well-designed DMLs. The current generation of high-quality monitor loudspeakers can also get extremely close to this ideal.

The sound power response of a loudspeaker is an extremely useful parameter that in many situations can act as a superior indicator of potential loudspeaker performance and can allow an indication of potential speech intelligibility. As we have seen, it is relatively simple to measure or compute the sound power response of a loudspeaker. With more and more devices being measured to ⅓ octave and 10° or 5° angular resolutions for CAD program device libraries, this parameter should be provided.

Ironically, it is the lower-cost end of the market where this information would probably be most useful in practice. However, it would also find considerable application at the upper end, particularly as a tool for loudspeaker designers and specifiers. After all, if you have the polar and Q data (which no self-respecting spec sheet these days should be without) it only takes a couple clicks of a mouse and a spread sheet modification to provide the sound power spec.

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Peter Mapp is principal of Peter Mapp Associates, an acoustic consultancy based in Colchester, England. Mapp is S&VC's sound reinforcement consultant and can be contacted at petermapp@binternet.com.

THE MATH BEHIND SOUND POWER Measuring Sound Power Lw

We all know that the direct sound level from a loudspeaker can readily be calculated from a knowledge of the 1W/1m sensitivity value by using the inverse square law (20•log r). However, how can we calculate the reverberant sound level in a room? Knowing this would enable us to immediately calculate the direct-to-reverberant ratio of either a single loudspeaker or a speaker system. This, in turn, would enable the potential intelligibility to be estimated and give an idea of the overall frequency response to be gained.

We can calculate the reverberant sound level using one of the most basic acoustic equations:

Lp = Lw + 10_log (Q/4š r2 + R/4)

But, of course, we need to know Lw. We can measure this using three methods, based on (1) reverberation room, (2) an anechoic chamber or (3) sound intensity.

In practice, either the reverberation chamber or anechoic measurement methods tend to be used. Where a reverberation chamber is available, the sound power can be calculated from a knowledge of the diffuse sound pressure level (Lp), the reverberation time and the volume of the room. Lw can then be calculated from the expression derived from the equation:

Lw = Lp_rev + 10_logV - 10_logT - 14
Where Lp_rev is the spatially averaged reverberant or diffuse sound level, V is the volume of the chamber, and T is the RT60.

Now if we also measure the nominal electrical (audio) power taken by the loudspeaker (from a knowledge of the applied voltage and impedance or current) and use calibrated sound pressure level and electrical measurements, then we can refer the measured value back to the reference power level of 10^-12 watts and end up with a useable value of Lw. Alternatively, if an anechoic chamber or a time-gated measurement system such as TEF or MLSSA is available, then Lw can be derived from calibrated polar measurements and the computed directional Q or Di value of the loudspeaker:

Lw = Lp - 10_logQ + 20_logR + 10.8 dB