Think Pieces

Considering the amount of careful research, cautious theorizing and wild speculation that have been lavished on the amplifier power question, we should expect to be considerably closer to the answer in 1962 than we were five years ago. This does not seem to be the case.

We have instruments for measuring sound pressure levels in the air, for measuring electrical power, and for analyzing distortion content to the third decimal place, and the literature is full of learned dissertations on the structure of musical sounds, their behavior in concert halls and living rooms, and the relationships between ears and the sounds around them. Yet one audio expert still maintains that 0.5 watts of amplifier power is all you ever need, while another says 50 watts is barely enough. Who is right?

As is often the case in such a diagonal disputation, both are partly right. One source of the widespread disagreement stems from the lack of any standardized criteria for judging power requirements. Thus, one expert may be stating how much power we need to produce a certain volume of sound during crescendos, while the other may be telling us how powerful an amplifier we must have before any further increase in available power ceases to yield any perceptible improvement in sound. On the other hand, another expert—the field is thick with them—might be figuring power requirements on the basis of a high-efficiency speaker system like the Klipschorn, while yet another expert may have decided that the only speakers worth listening to are low-efficiency types like the AR-1, so he bases his estimate on its power requirements.

All are legitimate approaches, but it is obvious that no one of them can supply a universal answer. Hence the compounded confusion.

Let's get one thing straight at the outset: "Need" has no bearing on the matter. It is senseless to ask how much power we need, because the answer is "none." We don't need high fidelity, when it comes right down to that. Nobody would die, no governments would collapse, no panics would ensue if, all of a sudden, high fidelity had never been.

All right, then, how much power should we have? Simply stated, we should have enough power to reproduce the desired sound at the desired level without exceeding a certain limit of distortion. This reads like a masterpiece of evasion, but it is a step in the right direction, for no expert will disagree with it.

But what level is the "desired" level? Background music level, foreground listening level, or the kind of ear-shattering level that a conductor might hear from his podium?

The hi-fi system owner who does not plan to use his rig for anything except background music can just forget all about power requirements. At very low listening levels, the ear's powers of discrimination are poor, so any amplifier that is sold under the guise of high fidelity will do. A cheap 5-watter will be adequate, and it isn't too important if its distortion is fairly high, because nobody really listens attentively enough to background music to notice its sound.

The only time we benefit from high fidelity is when we concentrate on the program, because that is when we start to get finicky about the sound. Our ears are most responsive to upper frequencies when the sound is loud, and it is at high levels where a hi-fi rig's distortion is prone to be most severe. If the amplifier is clipping the tops off peaks at high listening volume, the resulting raggedness of sound is much more audible than it would be were the amplifier doing the same thing at a much lower volume level. This, of course, helps to befuddle the issue, because the higher the listening volume, the lower the amplifier's distortion must be in order to sound pleasant. And we all know that the harder we push an amplifier, the more distortion it generates.

So, for the purposes of this article, we are going to assume that you will, at least occasionally, play your system at foreground level.

What about orchestra-in-the-room level? Although a popular advertising gambit, this is an absurd notion. To be mundane about it, there simply isn't room for a symphony orchestra in the average home, so even if it were possible to re-create the original volume of the orchestra as heard from the conductor's podium—which it is, but it takes scads of power and a highly efficient speaker—the effect could not be realistic. It would also be very un-neighborly. A solo performer, or a chamber group, could be in your living room, and sounds very convincing when so reproduced. But recording engineers realized long ago that orchestra patrons listen from out in the hall rather than from the podium, so they do their microphoning to convey as well as possible the illusion of listening from a mythical "best seat in the house." Their recordings sound best when reproduced to scale; higher volume levels make them sound overblown and unnatural.

As sound waves travel away from their source, their total acoustical power remains essentially the same, but as each wave spreads out over a wider area, it thins itself out. Thus, the actual intensity of a sound some distance from its source will be considerably lower than its intensity right at the source. For this reason, we measure sound intensities in a concert hall in terms of variations in air pressure (or the sound pressure), rather than in terms of watts of acoustical power. The original power at the source can then be computed, if desired, by a simple formula based on the fact that sound pressure weakens by a square root function as its distance from the source is doubled.

Sound pressure readings are made using a special microphone probe and a meter that resembles a tape recorder's VU meter but is calibrated in dynes/cm² of pressure or in decibels above the threshold of human hearing. The sound meter shares the same shortcoming as a VU meter in that its indicator needle, having some inertia, does not respond fully to transients, but gives an average (or RMS) reading.

The RMS level of sound during an orchestral crescendo, as heard from a fairly close seat in the concert hall (row C, for instance), measures about 100dB on a sound level meter. The acoustical power (not electrical, please note) needed to create this sound level, at a distance of 15 feet from a loudspeaker in a 10' by 15' by 20' room, is on the order of 0.4 acoustic watts.

If we used a 100% efficient speaker (which is unlikely, because there's no such thing), we could recreate the RMS power of the original sound with 0.4 watts of electrical power. To find the amplifiet power required to get this acoustical power from a practical speaker, we simply multiply the reciprocal of the speaker's efficiency rating (in percent) by 40 (footnote 1). Thus, for a 10% efficient speaker, we have: 40 x ¹/₁₀W, which works out to 4 watts. For a typical "low-efficiency" speaker of about 1% efficiency, we would need 40 watts of amplifier power to produce 0.4 acoustical watts.

The power figure derived by the above calculation represents the minimum amount of RMS power needed to reproduce an orchestral crescendo at its original measured sound pressure. The figure will apply as a total power requirement for both channels of a stereo system, but it will not apply for a monophonic system, because mono sound of a certain measured pressure level does not sound as loud as the same level when the reproduction is stereophonic. This means that, in order to reproduce monophonic material at the subjective level encountered in the concert hall, we need more power than would be indicated on the basis of sound level meter computations.

How much more is a moot point, because the disparity between stereo and mono power requirements varies with the program material, the way it was microphoned, and the acoustics of the listening room. It usually works out to about a 1–2dB difference, which seems negligible until we remember that it takes double the power to raise the listening level by a mere 3dB. To cope with a 2dB increase, we must up our original power estimate by a factor of about 1.6. Hence, if our original figure came out to 4 watts, we would have to multiply this by 1.6 to get our power requirement for monophonic listening, and this would come out to 6.4 watts for the 10%-efficient speaker.

The formula that we described for arriving at our minimum RMS power figure assumed that the loudspeaker radiated its sound in all directions away from the source. In truth, some speakers don't. The best loudspeakers for small-room listening are direct-radiator types, simply because they do radiate the sound over a broad area. But horns. which usually behave best in very large rooms, tend to direct most of their output forward, so a higher proportion of the radiated sound goes directly toward the listener. This would tend to reduce the power requirement even more for a horn-loaded system, but the high efficiency of the average horn puts its power requirement so low to begin with that it is pointless to quibble over an extra watt or two, even though this may represent a doubling or halving of the computed figure.

An orchestral crescendo, or a full choral passage, contains transients that are fully 10dB higher than the average volume of the sound, as measured by a sound level meter. A 10dB increase in level represents a 10-fold increase in power, so how can we possibly hope to cope with this sort of thing? Fortunately, we don't have to. Recording studios and broadcast stations use peak limiters to keep these huge transients out of the received signal, and tape recorders have their own built-in limiting action. Transients are high- frequency phenomena, and tape will saturate instantly if a strong treble impulse is fed to it. The result is a shearing-off of the peak, and if the overload doesn't last too long, this won't cause any more audible disturbance than a good peak limiter.

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Footnote 1: It's a mystery to me where this number—40—came from. In any case, there's clearly something off in JGH's calculation here, although the answers he cites are correct. He should have divided the acoustical power by the speaker’s efficiency—so, 0.4W/0.1 for a speaker that's 10% efficient and 0.4W/0.01 for a 1%-efficient speaker, yielding 4W and 40W, respectively.—Jim Austin