For those looking to gain a deeper understanding of howaudio works, whether to make better-informed decisions or simply for the sakeof curiosity, it's useful to lay down some ground rules that govern how audiosystems behave relating to loudness and the decibel.
One of the most important concepts in audio is thedecibel, the unit of measure denoting the ratio of a change in level, whetherthat level is acoustic Sound Pressure Level (SPL) or electrical signal level.It’s abbreviated dB. As you may or may not be aware, the decibel (dB) scale isa logarithmic system, as opposed to a linear scale. Being aware of therelationships inherent in this scale is important for a variety of reasons, whichwill hopefully become clear by the time you reach the end of this article.
Rule #1: +3dB = 2x the amplifier power; +10dB = 10x theamplifier power
Going from 1 watt to 2 watts of amplifier power gains 3dBof additional output; that's a pretty good deal right? Again, going from 2watts of amplifier power to 4 watts gains an additional 3dB of output. Giventhe relatively low cost of amplifier power these days, buying a more powerfulamplifier is a no-brainer.
So now that we have a basic understanding of therelationship between watts and SPL, let's complicate things a bit: What ifthere is a significant price difference between an 80 watt amplifier and a 100 wattamplifier? Things can get a little hazy here. Manufacturers do have their waysof skewing their wattage ratings, so the first thing you need to do is makesure you are comparing apples to apples. In other words, the amplifier powerratings must be rated under the same conditions.
A manufacturer may choose to rate it the “old fashioned”way, per the 1974 FTC power amplifier rating requirements, which came intobeing at that time in order to do away with all the misleading and vagueratings schemes like IHF Power, Music Power, IPP Power, etc. The FTC standard requiredthat amplifier manufacturers state their output wattage over a specificfrequency range (usually 20-20kHz, for mid- and high-end units), at a statedlevel of % Total Harmonic Distortion (THD), with both channels drivensimultaneously, into a stated load impedance (4 or 8 or 16 ohms) after aone-hour preconditioning period at 33% power. It was a great standard.Unfortunately, it was never upgraded to take multi-channel home theaterreceivers or powered subwoofers or self-contained computer speakers and dockingstations into account.
These days, in the era of multi-channel home theaterreceivers, the “both channels driven simultaneously” requirement has beenmostly disregarded. Some of the ‘better’ brands will rate their 5- or 7-channelreceiver in “2-channel mode” per the 1974 specs, but then they give a vagueoptimistic rating for multi-channel operation. Worse yet, the FTC has abandonedany effort to bring specificity and accountability to power ratings, so theconsumer is really on their own when trying to compare the output specs fromdifferent brands.
Example: Receiver‘A’ may state “120 watts x 7 @ 1kHz .5% THD, 8 ohms,” but then in really smallprint say, “65 watts continuous x 2, 20-20kHz, .1% THD 8 or 4 ohms.”
Receiver ‘B’ may state, “90 watts x 7 @ 1 kHz, .3% THD, 6ohms,”, but not give a 2-channel 20-20k rating at all.
Good luck comparing those. Actually, it’s quiteplausible, given the way the power is spec’d here, that these two units haveabsolutely identical output capabilities!
You can read more on this topic with our article ProductManaging Receiver Platforms .
Nonetheless, all else being equal (say, an incrementaljump in a specific manufacturers lineup), aside from 100 watts having a nicering to it, the “extra” 20 watts of power represents a rather insignificant 1dBstep.
What about a 200 watt amplifier versus a 400 wattamplifier? In an ideal world, and again all else being equal, you'd be lookingat another 3dB gain. There are some obstacles about going to 400 watts,however, as most speakers can’t handle that kind of power.
There are three broad categories as to why speakers canonly handle a certain power level:
- Thermal.Power is hot! Excessive power will heat voice coils to the point where they canexpand and bind up in the voice coil gap; heat can deform VC formers, softenadhesives, burn crossover resistors, all kinds of things. Speakers can toleratesome thermal abuse for short periods, but if too much heat builds up for toolong, the speaker will suffer a thermal-related failure….commonly called “burnout.”
- Mechanical.Excessive power input will demand that the speaker’s drivers try to move longdistances, perhaps farther than they were designed to. This can cause thedriver’s voice coil to “jump the gap,” or move so far that the voice coil comesout of the gap, misaligns, and can’t return to its original position. That’s anexcessive power-caused mechanical failure.
- Magnetic/Compression.This happens when the power input is so great that the speaker’s magneticstructure saturates and can’t convert the input signal into additional mechanicalenergy A speaker is a transducer—a device that converts one form of energy(electrical) into another (mechanical/acoustic)— and at this point, it stops“transducing.” At these extreme power levels, the speaker actually puts out a softer signal. This is known as compression, because the speakercompresses its output in response to a greater input signal.
Here is a useful table of a real-world situation with twolow-to-medium efficiency speakers in a normal listening room and a listeningdistance of about 9 feet.
Let’s say you have a speaker with a sensitivity rating of86dB 1m on-axis with a 2.83V input. Some might consider 86 dB to be on the“low” side for sensitivity.
But 86dB is really a pretty healthy level, much more thanbackground listening. It may not be loud enough in a dealer showroom, but inyour quiet listening room, you’d have to turn it down to answer the phone.
Now, you’ve got two speakers, so there’s some addition tothe 86 SPL figure because of that. You are also about 8-10 feet away from thetwo speakers (and somewhat off axis, to boot), so there’s some reductionbecause of that (the inverse square law, which says that SPL reduces by -6 dB asthe distance doubles). Throw in your room’s absorptive characteristics, anyopen walls that lead to the next room, etc, and what you’re left with is thatthe raw sensitivity figure for one speaker is a pretty decent number to workwith as to how loud two speakers will sound from your listening position with a2.83V (1 watt into 8 ohms, 2 watts into 4 ohms) input. There are a LOT ofvariables, obviously, but 86dB for 1 watt per speaker for a pair of speakersfrom your listening chair is not a bad estimate.
EditorialNote about Inverse Square Law & Real Rooms
We’ve all heard the -6dBinverse square law of SPL reduction for every doubling of distance but inreality that pertains to free space, or an anechoic chamber – which is a roomwithout echoes. Real world listeningrooms will see more along the lines of 3-4dB of loss for every doubling ofdistance. But for arguments sake, westick to the common -6dB figure for all of our calculations in thisarticle. Just recognize the real worldlosses should be much less, unless of course you live in an anechoic chamber orare listening to your speakers outdoor in free space.
Every doubling of power is another +3dB of loudness. So:
2 w = 89 dB
4 w = 92 dB
8 w = 95 dB
16 w = 98 dB
32 w = 101 dB
64 w = 104 dB
128 w = 107 dB
256 w = 110 dB
As you can see, even relatively modest amplifiers candrive these speakers to healthy loudness levels in a normal room.
The need for power escalates very quickly as you approach“lifelike” or “theater” levels of around 100-104 dB. Likewise,an average loud listening level of, say, 91 dB punctuated by a sudden peak of10-20 dB will make a huge instantaneous demand on your amplifier. This is whereyour amp can run out of steam very quickly. That logarithmic loudness-wattsscale we spoke about earlier really comes into play here.
So whatshould you, the avid reader, learn from all this?
Ultimately, there are twotakeaways:
a. More power is usually never a bad thing, but eventually you will reach a pointof diminishing returns when limited speaker capability, rising amplifier cost,and situational listening limitations (you’re in an apartment, for instance,and 105 dB peaks are simply not possible in your world) conspire together toput an upper limit on your amplifier power usage.
Interestingside discussion: There is a commonly held position among knowledgeableaudiophiles that says speakers—especially tweeters—are more often damaged bylower-powered amplifiers than higher-powered amplifiers. The reasoning goeslike this: in order to get higher SPLs, lower-powered amps are often turned upto the point that they put out a distorted signal. Since THD distortionproducts are whole-number multiples (“harmonics,” hence the “H” in the termTotal Harmonic Distortion) of thefundamental frequency, at higher frequencies like 5 kHz or 8 kHz, the 2ndharmonic distortion product will be 10 kHz or 16 kHz—barely audible asstand-alone test tones, never mind when they’re buried in the mix of an actual‘busy’ musical signal. But if the amplifier is putting out substantialdistortion due to “clipping” (being driven into severe distortion such that itsoutput waveform appears “clipped” when viewed on an oscilloscope), then thetweeter is being fed a very high level of ultrasonic energy, and they sufferthermal failure, even though the HF distortion may not be that audible to theuser.
This is why higher-powered amplifiers aresaid to be ‘safer’ than low-powered amps, because high power amps are far lesslikely to be pushed to the point of clipping and thus do not send high levelsof ultrasonic (but inaudible) energy to the tweeter.
On the opposite side of this issue are suchnotable engineers like Ken Kantor of AR and NHT fame. They dismiss this theoryentirely, saying that pure high levels of power—even so-called “clean” power—are the primary danger to speakers. Excessive heat is excessive heat, whetherit’s delivered by a distorted or undistorted signal, and excessive heat is whatburns out a tweeter’s fragile voice coil.
b.Don't fret small differences in amplifier power. All else being equal, you'renot going to notice a big difference between an 80 watt amplifier and a 100watt amplifier, except perhaps in your pocketbook.
Manufacturersoften increase the functionality and flexibility of the feature set as theymove up from one model to the next. The power ratings are often rounded intonice, “comfortable” numbers, so they makesense from a marketing standpoint. If model “A” is 75 watts x 7, thenmodel “B” with 2-zone capability, more HDMI inputs, better digital decodingcircuitry, and a logical step to a nice round “100 watt” x 7 rating gives modelsA and B a legitimate reason to co-exist in the lineup.
Asan example, the Onkyo TX-NR717 at $949 versus $649 for the next step down TX-NR616,are fairly logically priced, with power ratings and feature sets that seemperfectly commensurate with their asking price. Just be aware that in the realworld, 80 and 100 watts (of similar amplifier design) will sound virtually identical. But if you absolutelymust have that additional HDMI input, it’s priceless, no?
Rule #2: +6dB = double the sound pressure, 2x driverexcursion
This statement has a lot ofimportant implications. Certainly the notion that 6dB of extra output requiresdouble the driver excursion (all else being equal for sealed systems; venteddesigns are a bit harder to generalize about) should give some appreciation forwhat it takes to achieve higher output levels. For example, if you have a pair ofsubwoofers in an open field (above the ground, away from any major reflectivesurface), also known as full space or 4π steradians (a full sphere), and youstack them one on top of the other or put them shoulder to shoulder, you willtheoretically net a gain of 6dB versus running just a single subwoofer.
If you put that single subwoofer so its front radiatingpanel is flush with the wall (1/2 space or 2π steradians), you can alsotheoretically net a 6 dB gain. Back in the 1960’s, AR discovered that if theytook their speakers outside and buried them in the ground with their frontbaffles flush with the ground and then close mic’ed the woofer’s LF response,they’d get extremely accurate 2π measurements.
If you take that subwoofer and place it at the floor/wallintersection, then that’s called a ¼ space or π, and you’ll gain another 6 dBof output reinforcement.
Finally, if you put that single subwoofer in a corner atthe intersection of three room boundaries (1/8 space or ½ π), you cantheoretically net a 18dB gain relative to the subwoofer out in the open field,above the ground. Where is all this apparently “free” output coming from onemight ask? If you consider that a subwoofer is radiating energy in alldirections (bass is omni-directional in its perceived output, as opposed tohigher frequencies, which become more and more “flashlight-beam” directional asthe frequency increases), the answer should become clear: out in an open field,much of a subwoofer's output is wasted as it isn't being reflected back on you,the listener. Boundaries help to focus that energy where it's needed, thusboosting apparent output. Of course, it is worth keeping in mind that in thereal world, drywall and wooden stud construction doesn't make a"perfect" boundary, so the actual gains tend to be less than theorypredicts.
Nonetheless, the takeaway is this: Giving the subwoofersome “help” by placing it near reinforcing room boundaries will increase itsoutput without needing additional amplifier power and without requiring greaterexcursion (and hence getting more distortion) from the woofer.
A final thought for this section: by now you should begetting a good idea of what it takes to push the limits of performance: lots ofamplifier power and a robust driver to turn that into acoustic output. It mayseem a fool’s errand to chase a few more dB when the cost seems to go up out ofproportion to the benefit: after all, in terms of dollars per dB, a subwooferlike the SVS PB12-NSD would appear to have a much better cost to benefit ratiothan the PB12-Plus. To address this, we’ll need to discuss human perceptionswith respect to the dB scale, which is coming up shortly. However, going backto the above formula just remember: a 6dB gain equates to double the pressure,and when we’re talking bass, we’re talking about frequencies we can feel aswell as hear. Food for thought.
The SVS PB12-Plus. At under twice the priceof the PB12-NSD, it delivers on average 6dB more clean output relative to itslittle brother, i.e. twice the sound pressure. Combined with its superiorfeature set, the value becomes a little more apparent. But what do our earsmake of this?
Rule #3: Drop an octave = 4x the excursion (for sealedsystems) to maintain output; comparable to an increase of 12dB
Awareness of the above is perhaps the biggest argument Ican think of in favor of bass management. Consider that a single 5.25"driver in a sealed box needs roughly 1/2 inch of peak to peak throw to achieve100dB of output at one meter at 80Hz. That's quite a lot of driver excursion,and also a good argument for something a bit meatier than a small bookshelfspeaker if you're aiming for reference levels, which demand peaks of up to105dB from each channel, as measured from the listening position. Now imagineexpecting that poor 5.25" driver to reproduce 20Hz signals, which can bethe case if you choose to run it full range. You'll need 8 inches of peak-to-peakexcursion to maintain your 100dB output (16 times your 1/2 inch excursion at80Hz for a drop of 2 octaves); in other words, it isn't going to happen.
This relationship is also interesting from theperspective that it should give you some appreciation for what it takes to digdown deep. Once you start approaching the infrasonic realm, even a few Hz canrepresent a big leap with respect to the octave scale, and consequently therequirements from a subwoofer to reproduce such low frequencies with authority.To put it another way: 10Hz to 20Hz is a mere 10 Hertz, but it is a fulloctave, as is 10 kilohertz to 20 kilohertz, even though that’s 10,000 Hertzdifference. Octaves are 2:1. That’s what counts. A subwoofer designed to digdown to 20Hz with authority (Warp engines and exploding Death Stars, well belowthe musical range) will make a subwoofer designed to reach down to 32Hz (thelower limit of music, i.e. low “C” on a large pipe organ) look wimpy incomparison.
The TC Sounds LMS Ultra 5400. For deep bassreproduction, there is no replacement for displacement, and an 18” driver with33mm of Xmax has a lot of it!
AWord on Human Perception of Loudness
By now, your head may be spinning with numbers, and it’stime to bring it all home:
It’s great that 10 times the amplifier power canpotentially yield an additional 10dB of output, but what does all this mean toyou, the listener? The answer is that itdepends: our ears are complicated mechanisms whose sensitivity varies withfrequency, and it is important to remember that you can feel as well as hearsome sounds.
To start, it is worth taking a look at an equalloudness curve. You’ll notice that the threshold of hearingvaries by frequency (it takes a large amount of acoustic output for us to heara 20Hz tone, relative to 1kHz for example), and if you study the curvesclosely, you’ll being to see how the ear perceives jumps in SPL. At 1kHz, a10dB gain correlates with a perceived doubling of loudness in some frequencyranges. As you go down in frequency, however, you’ll find that the lines startto compress together: Instead of needing a 10dB gain to double perceivedvolume, you will need roughly 4-5dB in the deep bass frequencies. Further,remembering that we feel as well as hear deep bass, and taking into accountthat a 6dB gain corresponds with a doubling of acoustic pressure, one maybetter appreciate the previous example of the SVS PB12-Plus versus the PB12-NSD.
Forfurther reading on human hearing:
Human Hearing: How we Perceive Sound Summary Report
Forinformation regarding safe SPL levels, and protecting your hearing:
Tip of the Day: Protect Your Hearing
Ahandy SPL calculator, as well as a chart equating dB levels with various realworld examples:
SPL Calculator: How Loud will it get?
Conclusion
We hope that reading this article has given you clearernew perspective on the role and definition of “dB” and “loudness” in audio. Itcan indeed be a confusing subject, especially for those used to thinking in alinear scale. On the face of it, who would expect the difference between an 80watt amplifier and a 100 watt amplifier to be insignificant in the real world?Who would imagine that upgrading to a subwoofer with a mere 6dB more outputcould be so important in the perception of bass “impact”? Well, now that you'veread this article, you do. If you use this knowledge properly, it will help youmake more effective purchasing decisions and also aid you in setting up yoursystem. Happy listening!