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Acoustics Crash Course 2 - Reflectivity

By marktaw in Media
Mon Jun 24, 2002 at 05:21:59 PM EST
Tags: Music (all tags)
Music

With the proliferation of home recording studios, many more people have questions about room acoustics than before. This article is second in a series on acoustics for the home & studio. This time around: How what your room is made of affects sound & reverberation time in the room.

Acoustics Crash Course 1 can be found here.


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A Fun House Revisited

Take a look around you room. Look at the dark gray/black of the VCR and the DVD player. Look at the light color of the walls. The beiges of the couch, the blue of the drapes, the brown of the floor. Each of these contributes to the character of the room. If the walls were red, the room and everything in itwould take on the character of red.

The light from the plate on the table would be mostly white, but would contain somered content. Your eyes, or more accurately your brain,would compensate for the redishness of everything, and be able to recognize white objects such as papers. Even though it's influenced by the red of the walls, the mind can subtract this and see it as white.

This is a fairly accurate representation of how high frequency sounds act in a room.

Low vs. High Frequencies

Low frequency sounds are more affected by the size of the room more than the materials. There are several reasons for this.Both high and low frequencies are affected by the size of the room, but a 7 foot (161hz) wave will be affected by room size much more than a 1 foot (1130 hz) wave. Second, low frequency waves are less directional than high frequency waves. This is why woofers can be placed in any direction, while mid range speakers and tweeters should be facing the listener. Lastly, a 7 foot wave isn't affected much by two inches of foam covering the walls as a one foot wave.

The differences are often compared to waves and rays. A wave, like those made by a brick being dropped into a pond, are non directional, and may create standing waves if their length matches up with a room dimension. A ray, like light, is reflected in a very definite way, is much more affected by the materials it reflects off of, and can be redirected with some care.

There is no point where sound stops acting like a wave and starts acting like a ray. Both low and high frequency sounds have characteristics of both. The larger the room, the lower the cross over point. A larger room can support lower frequency sounds (longer waves) and room modes become less important earlier. I.e. a 50 foot room will be a concern to a 30 foot wave, but a 7 foot wave will generally find support. If not a 7 foot wave exactly, then a 7.14 foot wave. Compare this to my 18 x 11 x 8 foot living room. The room dimension to 7 is 8.

Since large rooms (music halls, many churches, etc.) are difficult to analyze and predict, it often takes a trained professional to build and treat them, though many of these theories can be applied to them. We're mostly concerned with mid sized rooms. Basically between bathroom sized and hall sized. Living rooms, Control Rooms, Recording spaces.

White, Black and Colored Objects

Okay, so now we have a room filled with objects. A white object is one that's good at reflecting a wide variety of frequencies of light. A black object is one that's good at absorbing a wide variety of frequencies of light. A blue object is one that's good at absorbing some frequencies (red and yellow, for example) and reflecting back others (such as blue).

This is the same for sound, some objects will reflect back most of the sound energy that hits them, some will absorbmost of thesound energy. Other objects will absorb at some frequencies and reflect at others.

The measuring challenge for high frequencies becomes not the size of the room, but the materials the room is built with and what's in the room. What sound 'color' does it have? Does it absorb more mids and reflect more highs, or absorb highs and reflect lows? Now, how do we measure how a material reflects sound?

Wallace Clement Sabine (1868-1919)

A the turn of the century a Harvard Physics professor by the name of Wallace Clement Sabine took a portable pipe organ and a stopwatch around and played various notes measuring the reverberation time of each under different circumstances. He then took throw pillows and put them in the room and measured the reverberation time.

These measurements give us the calculations we use today to measure absorbency. The Sabine unit and the Sabine equation. The modern version of Sabine's technique involves a special room and sophisticated measuring equipment.

You take an extremely reflective room. If you compare it's reverberation bare and with a known quantity of material in it you can learn how absorbent that material is. This gives us a number between 0 and 1. Zero is completely reflective, and One is completely absorbent. An open window (provided there's nothing outside to reflect sound back) would measure 1 - sound exits and never comes back in.

Since different materials absorb different frequencies better than others, they do this for six frequencies designed to give a general indication of the sound absorbency of that material.

If you're trying to calculate the absorbency/reflectivity of a room, you take the total Sabines for all of the objects in the room. Large objects are measured per square foot. Six square feet of carpet with a Sabine at a given frequency of 0.5 will have a total Sabine for the room of (0.5 x 6) = 3 Sabines. 15 square feet of door with a Sabine at a given frequency of 0.2 will have a total sabine of (15 x 0.2) = 3.

Companies that manufacture sound reinforcing materials publish their sabine numbers for various frequencies. With these numbers, some mathematical equations, and a knowledge of the size and composition of your room you can begin to calculate the reverberation times of your room.

The Math Bit

What we're measuring here is reverberation time. Before we figure out what the reverberation time of a room is, we need to come up with a definition for "Reverberation Time." A precise mathematical concept that can be plugged into a formula. The internationally accepted Reverb Time is the amount of time it takes for a sound to fall 60 decibels, RT60.

A decibel, "dB" is a logarithmic measurement. That is, 20 isn't twice as loud as 10. They've set it up so that every3 decibels is twice as loud. 13 decibels is twice as loud as 10 decibels. Therefore, 60 decibels is 20 times as loud as 0 decibels. Since the ambient level of sound in a living room is around 30-50 dB, in order to measure the RT60 time in your room we would need to activate a 110db sound and see how long it takes to fade to 50. This would really piss your neighbors off. 110db is 20 times louder than 50db.

Some sample decibel levels are as follows: Leaves Rustling: 20; Quiet Residence: 50; Conversational Speech: 60; Heavy Traffic: 80; Riveter: 120; Threshold of pain: 135; Propeller aircraft: 140. Please protect your hearing. You shouldn't be exposed to 100db of noise for more than 2 hours a day, 105 for one hour, 95 for four hours, 90 for 8 hours. You should also be conscious of your neighbors comfort. One person's art is another person's headache.

Rather than shooting a pistol off in a room, we'll use the Sabine equation to figure out the reverb time of the room. On the one hand we have the size of the room, and on the other we have the room's total Sabines.

The actual formula is:

0.049 V
------- = RT60
Sa

Where "V" is the volume of the room (lengthx widthx height) in cubic feet, "S" is the surface area of the room and "a" is the average sabine of the material. "Sa" is (S x a), or (Surface Area x average Sabines). You can add multiple Sa's together. The Sa for the floor + the Sa for the walls, etc.

The metric versionreplaces feet with meters, and the number in the numerator becomes 0.161.

0.161 V
------- = RT60
Sa

Wallace Sabine came up with the number 0.049, or 0.161 for metric by careful observation.

Knowing the dimensions of your room, all you need to know now are the Sabine units for the different materials that make up the room, and the Sabine units for anything in the room. With this you can calculate the Reverb Time of your room at six frequency bands.

Here is a Sabine calculator with charts.

Averages and Reality

Doing this calculation or every frequency between 18 Hz and 20,000 Hz would be exhausting, even for my aging Pentium 233 computer. Rather than do this calculation or every frequency, we do it for six average frequencies, and you'll see these on the packages of various sound treating materials. 125Hz, 250Hz, 500Hz, 1kHz, 2kHz, 4kHz. This gives us six broad areas an octave apart with which to do calculations.

Again, reality rarely conforms to mathematical models, and v.v. These are simpler models than those used to predict the weather. You may bring your umbrella or leave your suede shoes at home because they're predicting rain, but would you spend a thousand dollars on rain deflecting material for the house because of their predictions?

These calculations will get you in the ballpark, but you never know when afternoon thunder showers turns out to be evening drizzle, and when highsin the mid 70'sreally turn out to be highs closer to 85. Today's an especially good example, they predicted thundershowers and there's nary a cloud in the sky.

An Example

My living room is 18 x 11 x 8 feet. For now I'm going to ignore the two windows and two doorways and all of the stuff in between - the bookshelves, the couch, the people...

So that's 18 x 11 square feet of floor, 18 x 11 square feet of ceiling, and 18 x 8 x 2 + 11 x 8 x 2 square feet of wall. (length x height x 2 walls +widthx height x2 walls)That's 198 square feet of wood floor,198 square feet of ceiling, and 288 + 176 = 464 feet of wall, or 198 square feet of wood floor and 662 square feet of plasterboard. The volume of my room is 1584 cubic feet.

At 500hz, the Sabine unit for a wood floor is 0.10, and for plasterboard it's 0.05.

My formula is

0.049 x 1584 = 77.616
--------------------------------------- = 1.467 seconds = RT60
(198 x 0.10) + (662 x 0.05) = 52.9

My living room has a couch, coffee table, two windows, two doors, a wall full of bookshelves, a barcalounger type chair, a computer desk, two wall high CD racks, and very often one or more people. Certainly at least one person any time I'm interested in the RT60 of the room.

Oddly enough, despite all of the furniture which contributes to the total reverberation of the room, near the ceiling the RT60 is closer to the full 1.467 seconds, maybe even more. I can get this by moving around the room clapping. The clap will activate frequencies across a broad range. By listening carefully, I can hear aa high ringingecho near the ceiling.

Directivity

When sound hits a surface it can do one of three things. We've already covered absorption and reflection. The third thing is diffusion. Sound, like light, is very directional. When light comes in through your window, it illuminates a very specific area of the room, usually a floor or nearby wall. Sometimes in the morning or evening it will illuminate the far wall.

This light is then reflected around the room. Light also comes inin a diffuse way through the window, but the real strength is in that one spot on the floor where the direct sunlight or moonlight hits. If the floor is reflective, say there's a CD case or mirror on the floor right where the sun hits, then it will reflect in a very directional way, and illuminate a spot on the ceiling.

If instead of a a mirror, you placed a piece of frosted glass, it would spread light waves in many directions rather than just one. This is diffusion. A surface with a varied surface, like a cluttered bookshelf, will send sound in many directions.

Direct vs. Reflected Sound

Since high frequency sound is directional, in addition to the materials that are in your room, they can be affected by the placement of a few key treatments. Note that I'm talking about listening rooms and control rooms here, live rooms are a somewhat different story. The difference being that a listening room has a specific area the sound comes from - the speakers, and a specific area the listener should be sitting in - the "sweet spot." In a live room music often comes from multiple sources, and the audience is spread across a larger area. Live rooms also tend to be much larger than small rooms.

I'm going to remain neutral on the matter of whether or not you should add treatments to your room, and which treatments to add. There's a lot of controversy and discussion surrounding this topic. I'm just going to give you your options and let you make your own decisions.

A lot of people say you want to keep the really early 'direct' reflections away from your ears. This means treating the wall with absorbent. material at the point where sound will bounce off and hit your ears. If you take our fun house example, shining a flashlight at a wall will cause the beam to bounce off the wall. Aiming it the spot where light hits the speaker is the place you should treat.

The easy way to figure out this spot is to have a friend over with a mirror. Have him or her hold the mirror flat against the wall and move it around until you can see the speaker in it. This is where you would place your treatment. You would do this for all surfaces - behind the speakers, left and right walls, back wall, floor and ceiling.

Another way of removing early reflections is 'near field monitoring.' Essentially, you sit so close to the speakers that they dominate your sound field. By the time the direct sound fades away, you only have the later reflections.

The other camp, a much smaller set of people,says that these direct sounds are important to your conception of the music and treat the later reflections rather than the earlier ones. Dave Moulton leads this pack and developed the "Moulton Room."

The Moulton Room consists of a serious broadband absorber behind the speakers, lateral (side to side) room symmetry, and a large diffuser at the back of the room. This way your ears still benefit from the early reflections, but the reflections off the back wall are diffused back at the side walls, and later reflections off the front wall are nonexistent. The decay time in a room like this is extremely low.

How and whether you treat your room is a choice I leave up to you. I know I mentioned room symmetry in a Moulton Room, but both sides agree on this point. I just mentioned it because Dave makes a point of it whenever he talks about a Moulton Room.

Summary

High Frequency sounds are less affected by room size than by the room materials. This is because over any given octave, there will be many more activated room modes at high frequencies than at low frequencies giving an average level of support, where as at lower frequencies you get large peaks and valleys.

High Frequencies also behave more like waves than low frequencies, and care very much which direction the speaker is pointed in. They also bounce off walls in a predictable directional way.

Tofigure outthe Reverb Time(RT60) for a room across frequencies without sophisticated listening equipment you can calculate it using the Sabine equation based on the room dimensions and materials of the room. Different materials will have a different reflectivity/absorbency ratios (Sabine units), and it will differ for the same material across frequency ranges.

The reverb time is an estimate, just like the weather. It will certainly help you get an idea of the characteristics of your room, but reality often differs from mathematical models.

When sound hits a surface it will be absorbed, reflected, and diffused to different degrees. If reflected, it will bounce off at an opposite angle, just like light. If the sound hits a wall at 70 degrees off center, it will bounce off in the opposite direction at 70 degrees off center.

Because of the directionality of high frequency sound, it can be treated by placing absorbent. material on the wall where the direct sound reflects off and heads towards your ears. Another option would be to place absorbent. material on the entire wall behind the speakers, and diffusing material on the back wall.

Here is a Sabine calculator with charts.

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Acoustics Crash Course 2 - Reflectivity | 14 comments (9 topical, 5 editorial, 0 hidden)
Awkward sentence, but +1 section (none / 0) (#1)
by czth on Mon Jun 24, 2002 at 03:58:08 PM EST

Low frequency sounds are more affected by the size of the room more than the materials

I'd perhaps say that as "Low frequency sounds are affected more by the size of the room than by the materials in it." Too bad the story just dropped out of editing.

Generally looks like a well-written article, like its predecessor; +1 section.

czth

Rays vs. Waves (none / 0) (#7)
by Primavera on Mon Jun 24, 2002 at 05:39:27 PM EST

In the second paragraph of the summary do you mean "High Frequencies also behave more like rays than low frequencies," based on the comments in the Low vs. High Frequencies section about rays being directional, having predictable reflection characteristics etc.

Doh! (none / 0) (#9)
by marktaw on Mon Jun 24, 2002 at 11:52:57 PM EST

Another thing the spell check doesn't get for you. =(

[ Parent ]
Correction about decibels (5.00 / 1) (#8)
by jwb on Mon Jun 24, 2002 at 06:34:14 PM EST

You state that a 60dB attenuation is 20 times louder than 0dB, but this is not true. 60dB is one million times louder than 0dB. I have no references, but decibels are 10 * log10(ratio). In this case, the log10 of the ratio is 6, therefore the ration must be 10^6, or one million. 60dB is one-million-to-one.

Oops (none / 0) (#10)
by marktaw on Tue Jun 25, 2002 at 12:42:05 AM EST

I admit logarithms aren't my strong point. Some kinds of math I'm better at than others, but you're absolutely right.

10 log 1,000,000 = 60 dB

I'll strive for better fact checking in the future.

[ Parent ]

Poor marktaw (none / 0) (#11)
by p3d0 on Tue Jun 25, 2002 at 03:50:45 PM EST

The ironic part is that, in the very same paragraph, you had just finished telling us that decibels are logarithmic rather than linear. :-)
--
Patrick Doyle
My comments do not reflect the opinions of my employer.
[ Parent ]
Yep (none / 0) (#14)
by marktaw on Sat Jun 29, 2002 at 05:53:52 PM EST

I'm never going to live this one down.

[ Parent ]
dB is a mess (none / 0) (#12)
by ishark on Thu Jun 27, 2002 at 04:27:34 AM EST

It depends what dB you're talking about.

I'm not familiar with acoustics, but in electronics you have a coefficient of 20 (20 dB attenuation is 1/10) while in optics it's 10 (10 dB attenuation is 1/10).

[ Parent ]

power vs energy (none / 0) (#13)
by uhoreg on Fri Jun 28, 2002 at 02:38:57 PM EST

In acoustics it's 10. I remember hearing that the difference between the two dB's is whether you're talking about power or energy. One of them (I forget which, and I have too much of a headache right now to think and try to figure out which is which) is essentially the square of the other. So when you take logs, the square comes out and becomes an extra factor of two.

[ Parent ]
Acoustics Crash Course 2 - Reflectivity | 14 comments (9 topical, 5 editorial, 0 hidden)
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