KEF & HOFMANN’S IRON LAW

All subwoofers have to conform to Hofmann’s Iron Law and the KEF KC62 is no exception however KEF’s White Paper states that “Iron Laws cannot be broken, but they can certainly be bent.” So I guess we should take a look at Hofmann’s Iron Law and how it applies to the KC62!

Hofmann’s so-called ‘law’ of low frequency reproduction was coined by Joseph Anton Hofmann, who was one of the three founders of KLH Loudspeakers, a company that in its hey-day was the largest loudspeaker manufacturer in the world. In fact, the first letter of his surname was the ‘H’ in KLH. The other two initials were contributed by Henry Kloss (who helped found Acoustic Research before KLH and later founded Advent), and Malcolm Scollay Low (who had also helped found Acoustic Research and after leaving KLH would go on to found Evans and Sutherland Computer Corporation and become a pioneer in digital recording and computer graphics.)

It’s important to use Hofmann’s middle name because his father was none other than Josef Casimir Hofmann, one of the greatest pianists who has ever lived. And if that sentence made you stop in your tracks, consider that no less a pianist (and composer) than Sergei Rachmaninoff said Hofmann was the ‘greatest pianist alive’, Ralph Berkowitz said he “had the greatest technique of any pianist” he’d ever heard, and Anton Rubinstein thought that Hofmann was such “an unprecedented talent” that he took him on as a student — the only pianist he would ever teach.

On the merely ‘technical’ side, Josef Casimir Hofmann was also one of the first

pianists ever to be recorded (on an Edison cylinder) and was also a prolific inventor, with more than 70 patents to his name, including patents for pneumatic shock absorbers for cars and airplanes, windscreen wipers, and a device to record dynamics in reproducing piano rolls (unfortunately invented just as piano roll companies went out of business). He also patented improvements to piano actions that were later incorporated into Steinway pianos.

His son Joseph Anton Hofmann’s Iron Law essentially states that three important attributes of any loudspeaker system are inextricably linked: low-bass reproduction, enclosure size and sensitivity (efficiency) in such a way that it is impossible for a single design to satisfactorily deliver all three.

He said that optimising any two of these attributes would inevitably compromise the one that remained. “A designer who wants good, deep low-frequency sound and high sensitivity can obtain these goals, but they will have to use a large speaker enclosure,” he said. “Similarly, if a designer is forced by space constraints to use a very small cabinet, and they aim to get good, deep low-frequency sound, sensitivity will inevitably be compromised.”

It’s really a variation of an old business adage, one that’s so well-known you’ve probably seen it on a sign in a business in your neighbourhood: “We offer three kinds of service: Good – Cheap – Fast. You can pick any two.” Meaning that if it’s fast and good, it won’t be cheap. If it’s fast and cheap, it won’t be good. And, of course, if it’s good and cheap, it won’t be fast. If you studied project management at college, you probably learned these principles as the ‘triple constraints’ of any project: time, cost, and its scope or quality.

Of the three variables in Hofmann’s Iron Law, the one that’s the hardest to bend is the one that involves ‘good, deep, low-frequency sound.’ This is because of a very basic law of physics which states that if a bass driver can produce a sound pressure level of 90dBSPL at a frequency of 50Hz by moving back and forwards a particular distance (say, x), then for that same driver to produce 90dBSPL at 25Hz, the cone would need to move backwards and forwards a distance of 4x. That is, when the frequency is halved, cone excursion must be increased FOUR times (not two, as you might have guessed).

The factor of 4 comes about because sound pressure is a result of a cone’s acceleration. So it’s the rate of change of its velocity. The rate of change of a sine wave increases with its frequency: the faster it oscillates, the more change. So the rate of change of excursion (i.e. velocity) increases with frequency of oscillation. Half the frequency also halves the rate of change. Acceleration is the rate of change of rate of change, hence the factor of 4.

The problem for a typical cone speaker is that a good Xmax for a high-quality bass driver would be about 10mm. So if it were using this Xmax to deliver a 50Hz signal at, say, 90dBSPL, it would need to travel 40mm in order to deliver exactly the same SPL at 25Hz. Clearly impossible.

If, on the other hand, you decide to use the driver’s Xmax to deliver a signal at 25Hz, this means that in order for the response to be flat down to this frequency, the cone will only move 2.5mm at 50Hz. This won’t be very loud at all. So you can get flat response between 50Hz and 25Hz, but only if you accept that undistorted sound pressure levels will be compromised.

So, in the words of KEF’s White Paper: “When designing a small subwoofer, the choice has to be made between high efficiency and low frequency extension. Both are very desirable features for a subwoofer. To create a subwoofer that can deliver the maximum performance for the minimum of space, KEF R&D worked to push the compromises as far as possible. After all, Iron Laws cannot be broken, but they can certainly be bent.” #