DIY Acoustics Part 2: Modal Frequencies and Diffusers by Jake Hartsfield

JANUARY 20, 2010

DIY Acoustics Part 2: Modal Frequencies and Diffusers by Jake Hartsfield



Jake Hartsfield is a <a rel="nofollow" href="http://www.jakehartsfield.com/" target="_blank">songwrite</a>r, <a rel="nofollow" href="http://www.facebook.com/Jakestudio" target="_blank">producer</a>, touring sound engineer and a member of the TuneCore Marketing Team.

As we further explore acoustics and how to treat your listening/mixing room, we get into room modes, resonant absorbers, and diffusers. Every room has resonant frequencies along each of its axes that are directly related to the length, width, and height of the room. This article will explain how to calculate problem frequencies based on the dimensions of a room and how to solve boosts in the lower frequency range caused by them. We will also touch on diffusion • when and where it should be used and what objects make great diffusers.



Room Modes and Problem Frequencies

So you’ve been mixing in a small to medium sized room. You’ve got foam all over the walls (or hopefully, you’ve got something like OC703 now • read Part 1), so the room sounds pretty dead. You think you’ve got all your acoustic problems solved. But for some reason, your room sounds uneven in the lower frequency range. You hear a lot more bass when you stand back than you do when you’re sitting in your mixing chair (or vice versa). Why would this be?

The dimensions of any room will create resonant frequencies and standing waves that will create acoustic distortion and harm the frequency response of the room. Low frequencies (20 Hz • 300 Hz) like to resonate in rooms whose dimensions match their frequency length. By understanding which frequencies are likely to resonate in your room, you can predict what kind of acoustic treatment you need to help improve your room response.

Here’s a simple equation based on the speed of sound that will help you find the exact modal frequencies of your room based on the dimensions. (Don’t freak out, you can use a calculator!)

Frequency (f) = 1,130 / (d x 2)

1,130 (ft. per second) is the speed of sound. D is the distance between opposing parallel walls in your room. The third dimension (height) is the distance between the floor and the ceiling.

Simplified even more, we have:

Frequency (f) = 565 / d

So, if we substitute 10 ft. for d, we get 56.5 Hz. That means your room will resonate at 56.5 Hz on this particular axis.

In a room that is 18 ft x 10 ft x 8 ft, we can calculate the three fundamental (first) modes in the room along each of the three axes.

565 / 18 = 56.5 Hz

565 / 10 = 47.1 Hz

565 / 8 = 72.2 Hz

But we’re not done; each axis has a series of modes. There are also resonant frequencies at multiples of each fundamental frequency. So where 56.5 Hz is the fundamental, 113.2 Hz is the second mode, 169.8 Hz is the third mode, and so on. Below is an example chart for the 10’x12’x9’ room we’ve been theoretically discussing, showing each of the modal frequencies for the three axes. Ideally, the modes should be spaced apart evenly, but based on the room dimensions, some modes will be closer together and there will be some gaps between modes. The closer modes will create a boost near those frequencies and the gaps will have the opposite effect.

Modes begin to get much closer toward higher frequencies, allowing a smoother response. As a result, the problem frequencies are generally below 300 Hz where there is more space between modes.

<p style="text-align: left;"><img src="http://api.ning.com:80/files/dmdlEdcbqaaCHvzxhfPaYbSskxNncIRl0bbvRAQG*tKBzmvR60py0G-tnAGLoEI*z6fudj0JF3wkAReKf*28CyYnRL8p5WdY/6a00d83455f72e69e2012876f135f2970c800wi.png" alt=""/></p>


This example room actually turned out to have great mode spacing. The main problem frequency here is 282.5. All three axes are resonant at this frequency, which could cause a boost around that frequency. There’s a lot of space (31.4 Hz) between 282.5 Hz and the nearest modes, so that will accentuate the boost. One possible solution to this boost at 282.5 Hz would be a few well-placed tuned Helmholtz resonators or panel (Diaphragmatic) absorbers.

Low Frequency Resonant Absorbers

Lower frequencies are difficult to absorb, because the absorber theoretically should be ¼ of the wavelength to be the most effective. When dealing with specific problem modal frequencies, sometimes the best type of absorber to use is a panel absorber or Helmholtz resonator that resonates at the desired frequency and absorbs the energy. Helmholtz resonators are airtight boxes tuned based on volume to resonate at a particular frequency. Similarly, panel absorbers have a diaphragm (the outward-facing side of the box) that is tuned to vibrate at the desired frequency based on depth of the box and thickness of the panel.

Both resonators are usually built with absorbent material on the inside to help absorb the sound as it resonates inside the unit. In the case of the panel resonator, it’s important that the absorbent material does not touch the back of the panel, so that it is able to resonate freely.

I promise I’m not getting paid to say this - F. Alton Everest’s Master Handbook of Acoustics has an incredible chapter on panel resonators and Helmholtz resonators, with charts that show how to tune a resonator to a specific frequency by varying the thickness of the panel and the depth of the space behind it.

There are also tons of other great resources online with diagrams explaining how to make your own resonators.

Diffusers

When sound hits a flat surface straight on (at a 90 degree angle), such as a wall, most of it is reflected back exactly where it came from. When mixing, this can create a slap echo effect, especially coming from the wall directly behind your mixing position. This can often be treated with absorbent material, but too much absorption can cause your room to sound dead and lifeless. Another way to deal with this reflective surface is to use diffusers to scatter the reflections in other directions all around the room.

Diffusers can help spread reflections out, helping flatten your frequency response in the higher range, and make your room sound bigger than it actually is. A room cannot only be treated with diffusion • it is often added after a room has been treated with absorption to add a little life back into the room and to polish the overall room response at the listening position. Diffusers are most often (and most effectively) placed on the wall directly behind the mixing position, sometimes covering the entire wall.

There are several types of diffusers, the most popular being the skyline diffuser and the quadratic residue diffuser. Both are based on formulas derived from number theory that are supposed to provide the most even frequency response across the higher range. Most all diffusers are built with reflective material (often wood) with wells of varying depth.

The RPG skyline diffuser is most often floated from the ceiling above the mixing position to help diffuse first reflections from the ceiling.

RPG Skyline Diffuser:

<p style="text-align: left;"><img src="http://api.ning.com:80/files/wGu6jIuROZpnyJKPHr6LgSlV-xCMoa97WbgDfbLOSzpkfU57lUGodD3jTXm*HvUI3TZ82eQ3eK8Y3nXYv31whWB7hWB*J74s/6a00d83455f72e69e20120a7ee376d970b800wi.jpg" alt=""/></p>

Quadratic Residue Diffuser:

<p style="text-align: left;"><img src="http://api.ning.com:80/files/8KRSoezZKjZ0XaBgeJFua605JrBmG19gS-qXPowGMb11Pgna84mSySxWQ8l9STBprI7qhefGAQ8ZkoiDvGMzoDLt8J4YGbbs/6a00d83455f72e69e2012876f13754970c800wi.jpg" alt=""/></p>

I’m actually building a few quadratic residue diffusers of my own in the next week or so. I’ve already completed the design and bought & cut all of the wood and materials. It ended up costing about $90 each, and the commercial versions cost about $450. Email me if you want to see pictures of the project!



Resources

There are a lot of great sources for more information about acoustics, various DIY absorbers and diffusers, and room optimization techniques. Here are a few of my favorites:

Master Handbook of Acoustics (Fifth Edition) by F. Alton Everest

This is the Holy Grail of Acoustics • I guarantee it has everything you will ever need to know about the physics and practical application of sound and acoustics ☺

On the web:

Ethan Winer (CEO/owner, RealTraps) - <a rel="nofollow" href="http://ethanwiner.com/acoustics.html" target="_blank">http://ethanwiner.com/acoustics.html</a>

Real Traps - <a rel="nofollow" href="http://www.realtraps.com" target="_blank">http://www.realtraps.com</a>

GIK Acoustics - <a rel="nofollow" href="%20http://www.gikacoustics.com/education.html" target="_blank">http://www.gikacoustics.com/education.html</a>

RPG (Industry leaders in diffusion products) • <a rel="nofollow" href="http://www.rpginc.com/" target="_blank">http://www.rpginc.com/</a>

RPG Acoustic Articles: <a rel="nofollow" href="http://www.rpginc.com/news/library.htm" target="_blank">http://www.rpginc.com/news/library.htm</a>

Want support for your DIY project? Check out the forums on Gearslutz. Ethan Winer and Glenn Kuras (GIK Acoustics) regularly offer their opinions and advice on various acoustics forums • you can probably also find any question you have has already been answered by one of them.

Posted by TuneCore at 01:46 PM | <a rel="nofollow" href="http://blog.tunecore.com/2010/01/diy-acoustics-part-2-modal-frequencies-and-diffusers-by-jake-hartsfield.html" target="_blank">Permalink</a>