What you need to know about understanding frequency response curves of loudspeakers.

Here’s an essential archival article from Paul Diacomo, a brilliant writer and longtime Polk Audio executive who published many classic articles on hi-fi throughout the years. We are publishing it again here in the hope that a new generation of readers finds great value in his writing.

The Secret Behind The Industry’s Most-Cited Spec.

Here’s a quick quiz: which of these two speakers sounds better: Speaker A with a frequency response range of 45Hz to 18kHz or, Speaker B with a range of 20Hz to 25kHz? The truth is there’s simply not enough data in these numbers to know anything of value. Taken out of context and without other data, a simple set of numbers don’t tell you much about real world sound quality. But people make audio buying decisions based on published specifications, such as the frequency response spec, everyday. I’d like to demystify the process for you; let you in on a little industry secret about “The Frequency Response Spec.”

My Frequency Response

The Frequency Response specification attempts to describe the range of frequencies or musical tones a speaker can reproduce, measured in Hertz (known to old-timers as “Cycles per Second”). The range of human hearing is generally regarded as being from 20Hz, very low bass tones, through 20kHz (20,000Hz), the very highest treble. Presumably a speaker that could reproduce that range would sound lifelike. Alas, it is no guarantee. The most important determinant of a speaker’s frequency performance is not its width or range, but whether it’s capable of reproducing all the audible frequencies at the same volume at which they were recorded.

You don’t want the speaker to change the “mix” of tones; that would ruin the timbre of voices and instruments, making them sound unnatural. Ideally, you want the sounds that are on the recording to be reproduced as they were recorded, without the speaker changing the sound. To say it another way: if you made a recording of all the audible tones at the same volume and played that recording through a speaker, you’d want all the audible tones to come out at the same volume. In fact, that’s one way of measuring speakers. A signal that’s comprised of all frequencies at equal volume is fed into a speaker that sits in a room with no reflective surfaces. A calibrated microphone is placed in front of the speaker and feeds the speaker’s output into a machine that plots the frequency vs. amplitude as shown in Figure A.

Now take a look at the graph in Figure B. That’s the frequency response of the Erehwon Model 10, with drivers and tweeters made of pure Unobtainium (“Half the carbs, all the sound!”). The flat line on the graph indicates that the speaker is “flat”; it reproduces all the musically relevant tones at the same volume. That doesn’t mean that a “flat” speaker will play all recorded sounds at the same volume — bear with me here — it means that it will treat all sounds equally; it won’t impose its will on the music but will allow you to hear the music as it was recorded. Flat is good. Flat response means that the speaker reproduces sound accurately.

Frequency Response In Context

A big improvement would be a frequency response number that also includes the amplitude tolerance, expressed as “XHz-YkHz +/- 3dB.” This tells you that the amplitude of the speaker’s response relative to frequency does not deviate more than 3 Decibels from the center line. The “plus or minus 3dB” spec is regarded as a standard of sorts. The theory is that 3dB differences are “just perceptible,” so a speaker whose response curve lies within that tolerance window is a reasonably accurate speaker. Let’s see if that idea holds water.

If I had to choose strictly by the response curves, I’d choose speaker D because its amplitude variations are smoother and gentler. In contrast, speaker C’s amplitude variations are more extreme and “spikey.” Experience has shown speaker designers that those rapid changes in response produce a sound that is more fatiguing, less pleasing and subjectively less accurate.

My Response To Frequency

Now that you know the importance (and limitations) of amplitude variations in frequency response graphs, you might ask: “does the frequency range tell us anything at all?” Yes, it does. As long as you know the amplitude tolerance (+/- 3dB), the frequency response range or width tells you how high or low the speaker goes. A speaker rated as 20Hz – 25kHz +/- 3dB will play lower bass and higher treble sounds than a speaker that measures 40Hz – 20kHz +/- 3dB. I wouldn’t bet money that it would be the better, more enjoyable speaker, but at least I’d know something of value.

And now that you know how to interpret these numbers, you’re ready to run right out and buy a speaker just by looking at the response curve, right? I wouldn’t recommend it. Despite many advances in technology over the past 20 years, frequency response measurement is an imperfect science. The same speaker measured by two different labs may yield different response graphs. And some companies just plain cheat when they publish response curves. If it looks hand drawn, it probably was. (Yes, the graphs were hand drawn for illustration purposes.)

The Third Dimension
So far we’ve talked about frequency (the X axis of the graph) and amplitude (Y axis) but we left out an important third dimension: time. When a speaker responds to an impulse, for example a rim shot — “THWACK!” — it should start instantly and stop the instant the instrument stops making sound. If the speaker keeps vibrating or resonating and making sound after the source sound stops it’s changing, or “coloring,” the sound of the original recording. And that’s bad.

Figure F shows a bandwidth limited impulse signal. You can see that it starts and stops abruptly. Figure G shows that same impulse coming out of a speaker. You can see that the sound persists after the impulse input has stopped — it resonates or “rings.” The speaker is changing the timbre or character of the original recording. In order to see to what extent and at which frequencies the “ringing” is happening, we use a sophisticated computer algorithm called MLLSA (affectionately called “Melissa” by engineers who don’t date much) to measure the response of a speaker in frequency, amplitude and time. Figure H is a MLLSA spectral decay graph of a prototype speaker. The third axis of this graph is time, so graph lines closest to you are measurements taken later than the ones in the back. Think of it as a series of slices with each slice being a frequency response graph taken at a different point in time.

If we were to measure the perfect speaker the MLLSA graph would look like a straight line in back with no lines in front. Real speakers fall far short of this ideal and continue to resonate after an impulse has stopped, such as in Figure H. Figure I is a Polk LSi9, and we can see that the speaker stops responding sooner in the midrange than the speaker pictured in Figure H, indicating that the LSi9 is a better sounding speaker.

While no measurement technique can fully describe the subjective sound of a loudspeaker, MLLSA and other frequency response measurements are of great help to Polk engineers in developing better sounding speakers. Only a fool would design a speaker based on measurements alone and only a total fool would design a speaker based solely on subjective listening. A speaker that might sound good on a particular recording may in fact be flawed – it may have what is commonly called a “euphonic coloration.” It may be pleasing to the ear under certain conditions, but it sure ain’t right.

We use both measurements and subjective listening to design and evaluate speakers. The measurements save us time and are a great help in pointing us in the right design direction, avoiding mistakes that may come back to bite us later. The measurements give us a means of selecting which experimental designs are worth listening to.

But we have to be satisfied with the total subjective experience before a new design becomes a Polk Audio speaker. We spend countless hours listening to music and movies. Several experienced listeners have to listen to a proposed design and sign off on the sound before a model can even go into production. The Project Manager, Systems Engineer, VP of Engineering, Product Line Manager, and especially Matthew Polk, all have to agree that the prototype delivers the kind of rewarding listening experience that you expect from Polk Audio.

What’s Your Frequency?

You now know the secret: a frequency response specification is a very weak predictor of the actual performance of a loudspeaker. A frequency response chart can be more helpful, but it’s missing the important time measurement. You now know to look for overall curve smoothness and to avoid rapid swings in amplitude. Some magazines and review sites publish MLSSA graphs of reviewed speakers, and now you’ll understand how to interpret them. More power to you!

No matter how adept you might be at interpreting frequency response data, it should only be one data point among many in choosing a speaker. There is so much more to a speaker’s performance than just its response – like its dispersion and imaging, dynamic range and detail resolution as well as size, cosmetics and price. Looking at good frequency response data can help you eliminate speakers with obvious and obnoxious errors. Once you’ve eliminated the boom & tizz pseudo-fi speakers, you can settle down to careful listening and making a more informed choice.

How Polk Specifies Frequency Response

Polk Audio publishes two frequency response specifications: “Overall” and “-3dB.” “Overall” describes the frequency range limits of the speaker within an amplitude drop off of 9dB. Any frequency reproduced more than 9dB down from the rest of the frequencies will contribute little to the sound. The “-3dB” spec describes the frequency range limits of the speaker within an amplitude drop off of 3dB.

I just wrote this big article making the case that these kinds of numbers are not terribly useful in making buying decisions. So why does Polk use them? For better or for worse, these numbers are the norm in the audio industry.

To not publish them would leave an impression that our products were not competitive. A better question would be: why don’t we publish frequency response and MLSSA graphs in addition to the simple numbers? We feel that these graphs would not be meaningful to the vast majority of consumers.

It takes years of working with measurements and loudspeakers before you get a good sense of how the graphs correlate to subjective sound quality. Incorrect interpretation of graphs can easily lead to misinformation and bad choices. Finally, the variation in measurement techniques can make comparing graphs from two different labs or manufacturers unreliable and misleading.

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This article originally appeared at ecoustics.com and has been published here with permission.