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The Long And Short Of It: Acoustic Wavelengths

Understanding the nature of wavelengths can aid in optimally setting up and operating sound systems...

Most sound practitioners know that low-frequency wavelengths are much longer than high-frequency wavelengths. But because we can’t see them, to what level do we really understand them?

This is an important subject because understanding the nature of wavelengths can aid in optimally setting up and operating the various types of sound systems that most of us come in contact with.

Let’s look at the physical differential between low frequencies and high frequencies. They are quite radical, in the sense that we do not often encounter such a degree of variance in other fields.

A 20 Hz wavelength is about 60 feet long, or 720 inches. A 20 kHz wavelength is 0.055 feet long, or 0.66 inches. That’s an enormous differential, a ratio of 1091:1, or three orders of magnitude.

What does the length of a wave really mean? In two words, a lot. Sound travels at the relatively low speed of approximately 760 miles per hour in air, compared to light, which travels at approximately 671 million miles per hour.

A long, low-frequency wavelength requires some time to propagate, which means that it must first develop in the atmosphere before the sonic energy can be perceived as a note or tone. A 20 Hz wavelength takes 1/20th of a second to propagate, which is equal to 50 milliseconds.

By contrast, a short, high-frequency wavelength takes very little time to propagate and become audible, and can do so in small spaces, whereas a low-frequency wavelength needs adequate space in which to develop. This is why studio control rooms and other critical listening environments, particularly those that are on the smaller side, will often use bass traps to even out the bass response. Bass traps are acoustic energy absorbers designed to dampen low-frequency energy in order to provide a flatter, more even, low-frequency room response by reducing LF resonances.

Low-frequency (above) and high-frequency waves.

When low frequencies propagate into an echoic room, which describes all rooms that have reflective surfaces, they generate standing waves. Standing waves are pressure nodes created when a sound wave reflected from a wall collides with the direct sound from the loudspeaker. At some frequencies the reflections will reinforce the direct sound, creating an increase in level, while at other frequencies the reflections cancel the direct sound, thereby lowering the level.

One or more bass traps, often located in the corners of the room for maximum effectiveness, will absorb the LF energy rather than let it reflect outward. Non-parallel walls and an angled ceiling can also help reduce standing waves. Incidentally, one reason that early trapezoidal loudspeaker enclosures were developed was to reduce internal cancellations. Within limits, the trapezoidal shape does exhibit certain advantages.

The differences in bass response from one room to another is one of the most apparent and meaningful effects that the room will contribute to the sonic quality.

On several occasions I’ve analyzed and equalized sound systems in large tents – once for Cirque du Soleil, another at a large business conference, and several times for general entertainment. Because tent walls are so flexible, low-frequency reflections are hardly evident at all. The LF energy literally moves the tent walls (you can feel it), thus being damped instead of reflected.

This certainly was a surprise to me after spending years tuning systems in concrete, steel, glass, and wooden structures. In the LF range it was similar to the response you expect to see when measuring outdoors. But unlike outdoors, mid and high frequencies showed pounced reflectivity and resonance, which is nearly the exact opposite of hard-walled rooms.

Waves & Ripples

Long low-frequency wavefronts can be visualized by imagining large tsunami-type ocean waves crashing into buildings on the shore; they do not “see” the building as an obstacle and simply pass around it (assuming the building is of sufficient strength not to be destroyed). This is why it works to hang subwoofers behind a line array; they also do not “see” the line array as a barrier.

Conversely, short wavelengths can be visualized by imagining small ripples in the water that will break up, or reflect, when meeting an obstacle. As a case in point, even the typical perforated metal loudspeaker grille has a reflective and diffusing effect on high frequencies, though it is fairly minor in most cases.

How does understanding wavelengths lead to better sound system management? By knowing approximate wavelengths for various frequencies, and even visualizing them, you can potentially make better choices when it comes to loudspeaker placement.

System design factors, such as controlling the distance between subwoofers and full-range loudspeakers, or planning the distances between one subwoofer to another, become clearer when you think in terms of frequency and wavelengths. One important topic is how the range of wavelengths will be affected throughout the crossover region from full-range loudspeakers (often flown) to the subwoofers (often ground stacked). When two sources are separated by a quarter wavelength or more, constructive and destructive interference will occur, depending on the position of the listener or the measurement mic.

With respect to crossovers, it’s important to understand that a 120 Hz crossover to the subwoofers (for example) does not only affect frequencies at 120 Hz. If the crossover slope is 12 dB per octave, which is common, then at 90 Hz and at 180 Hz, the half-octave intervals, there will still be a potential for cancellations – or beneficial summation – although it won’t be as pronounced as it is at the crossover’s center frequency. One of the loudspeakers will be 6 dB lower in amplitude while the other will be 6 dB higher, assuming that the crossover slope is symmetrical.

Yet while the cancellation or summation effect of the combined sources will be reduced in amplitude still, it will be present. This makes a good case for steeper crossover slopes, with 24 dB per octave or 48 dB per octave often being rapid problem solvers. But steeper is not always better, an involved discussion of it’s own outside of our scope here.

Noise Abatement

You may sometimes be called upon to control noise “pollution” with respect to neighboring structures or to adjacent events. These might be the “air walls” for adjoining meeting rooms in a hotel environment. Or perhaps more specifically, the occupants of the staff residences located behind the rear of the outdoor Greek Theatre at the University of California at Berkeley, who aren’t thrilled with high-volume, late-night concerts. In order to help control such problems you’ll benefit by knowing about wavelengths and their effect on radiated directivity.

This is not just conjecture; in 1982 I was asked by Bill Graham to help the Greek Theatre stay in operation. There was no easy answer at that time – prior to the advent of modern line arrays – but of course we did the best we could with the tools that were then available. The outcome was essentially to reduce LF output across the board and more drastically, reduce overall operating levels.

This issue gave birth to the SPL police in the San Francisco Bay Area, and at the end of the day, nobody was pleased. Fortunately, today there are better ways of dealing with that type of problem. Line arrays and cardioid subwoofers can greatly aid in keeping the sound where it is needed, and minimizing it where it is not.

Array Directivity

When planning the number of modules – and therefore the size of a line array or a conventional array – it will be easier to determine the required size of the array when you think about the lengths of the wavefront. An array must be quite large if the low-frequency energy is to be controlled and directed in the lower segment of the audible sound spectrum. A small array of four or five elements may control upper mids and highs adequately, but if it’s only several feet tall, it’s certainly not going to provide effective LF pattern control.

Various publications expound about line array length versus the frequencies that a line of drivers can control. A wide range of opinions are stated, sometimes varying substantially. Even the nature of the line array wavefront, whether it is cylindrical in nature – or not – is the subject of debate among loudspeaker manufacturers as well as non-partisan authors. It’s very difficult to determine which authoritatively stated opinion, or collection of opinions, should govern your system design choices.

Low-frequency wavefronts make it feasible to fly subs behind line arrays.

In support of practical applications, a good rule of thumb is that array size must equal at least a half-wavelength of the lowest frequency in which you’re seeking pattern control, but that’s just scratching the surface. A half wavelength will just begin to develop some semblance of control. If you’re looking to keep LF energy from bouncing off the rear walls, it’s wise to increase the array length to at least a full wavelength at the absolute minimum, and preferably several times greater.

Soon, however, this becomes impractical in the real world. A 100-foot-tall line array, which would be five multiples of 60 Hz, will presumably provide very effective vertical control, but is unlikely to be achievable in all but the most esoteric conditions.

DSP Support

There are things that level control of line array modules, time delay, and complex DSP frequency shading can do to potentially improve large-scale array performance beyond the obvious aspect of simply flattening the composite response.

Beam steering is one method that may be the answer to keeping array size manageable, while creating directional control that seems to defy the laws of physics. Beam steering is based on delaying some modules in relation to others, thereby increasing or altering the cancellation effect that is the very essence of how the line array principal works to control directivity. Complex DSP control is a field that’s developing rapidly, and is likely to offer continued improvements in performance for the foreseeable future.

It’s not an easy proposition to assemble and measure large-scale line arrays, let alone to attempt the thousands of variations, in an inert acoustical environment, that are needed to determine precisely what the effect of complex DSP intervention can – or cannot – achieve in performance advantages. Fortunately, computer modeling makes it much easier and less expensive to explore differing scenarios, and that is exactly what drives the majority of much present day research and development.

Getting Results

Arrays of various types have been with us for decades. Some have proven to be very effective, providing cohesive and consistent sound quality to large numbers of people, while others have been a poor attempt at assembling loudspeakers that have little business being used together in any sort of deployment, not even in a disjointed cluster. But progress goes on.

By understanding the fundamentals of sonic energy, which in large part is being able to grasp the nature of wavelengths, you can authentically evaluate marketing claims, make informed decisions when planning and deploying loudspeaker systems, and deliver optimal results to your audience.

This short introduction to acoustic wavelengths is just that: an introduction. To fully understand how the nature of sonic energy affects the wide range of situations that the practicing sound engineer might encounter, I encourage a serious commitment to learning and understanding acoustical principals, and how they relate to real-world applications.

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