ACOUSTICS AND ARCHITECTURAL DESIGN; The Great Indoors

Ted Uzzle

The primary responsibility of architectural acoustics is to exclude outside sounds that would disturb hearing conditions. This can be especially difficult when the noises produced by a particular venue are not higher in level than the potentially intrusive sounds coming from outside the building. In outdoor facilities or facilities that produce a high level of sound – as with open air-arenas and sports facilities – there is usually no trouble overcoming the noise that might otherwise infiltrate. Often, the more important noise-control task is preventing stadium noise from annoying neighbors.

Construction practices need to be tightened up considerably in venues that are more susceptible to outside noise. Attention must be focused on insulation choices, doorways, window treatments, HVAC and structurally borne sounds if the facility is attached in anyway to other buildings or units. Designing and building schemes for reducing noise and sound proofing is an involved topic, and this article will focus on understanding the mechanisms involved in sound’s behavior in rooms.

Temporal sound behavior

Sound in a room changes over time. (See Figure 1.) A sound source in a room is turned on at time t subscript 1, allowed to operate for an interval and turned off at time t subscript 3. Its duration is thus t subscript 3 – t subscript 1.

>From a listening position elsewhere in the room, we observe the sound >pressure produced as a result. At point B in Figure 1, the pressure wave >passes the listening position. It has arrived at time t subscript 2. We >now know the distance between the sound source and the listening position >is:

c / (t subscript 2 – t subscript 1)

where c is the speed of sound.

The sound pressure continues at the same level as the sound source continues to produce sound power. Soon the first, early reflections arrive at the listening position. These either add to or subtract from the pressure already observed, according to the phase relationships between the directly arriving sound and the reflected sound. They will usually add to some degree rather than subtract if the sound source is producing a rapidly fluctuating signal, such as random noise or speech. At points C and D in the graph, we see discrete increases in pressure as reflected sounds add to the direct sound.

At some time, t subscript 4 in this graph, a bundle of sound energy reflected from various room surfaces begins to arrive. From point E to point F in the graph, the pressure rises, not in discrete steps but in a somewhat shaky diagonal rise.

>From points F to G in the graph, the source and its room-wide reflections >are in a sort of equilibrium. The amount of sound power entering the room >from the source and the amount of sound power leaving the room are in >balance. Sound power might leave through an open window or door. It might >leave by being transmitted outside through a vibrating boundary panel >(re-radiated on the other side) or through the structure of the building. >It might also leave through dissipation, by being converted to heat at the >boundary of the room. We call these phenomena absorption; we will discuss >that a bit later.

What if the sound source contributed power forever? What if no power left the room? What if the room were perfectly enclosed, perfectly rigid and perfectly reflective? The room would explode when the enclosed sound power became great enough to break the boundaries and the structure that supports them.

The sound-pressure level between points F and G is greater than the sound-pressure level at point B. The difference in level is what used to be called room gain. That term has rightly fallen into disfavor because the room is a passive device and incapable of contributing gain to the sound power inside it. Although for some years the industry jargon adopted the semantic blooper, it is an important point: In sufficiently reflective rooms, the total sound pressure at many listening positions is greater than the direct sound alone.

At time t subscript 5, the equilibrium is broken because the sound source has been shut off. From point G to point H, the sound pressure drops. It drops at a rate (in dB per second) determined by the rate at which sound power is lost from or dissipated in the room. This is a characteristic of the room, having almost nothing to do with the sound source.

If the sound pressure drops 60 dB, the time interval t subscript 6 – t subscript 5 is the reverberation time. This is one of the most critically important acoustical characteristics of the room, and its relationship to the physical room is:

T=0.049 V/A

where T is the reverberation time; V is the room cubic volume in ft superscript 3, and A is the total absorption in the room, figured with customary units (feet). The 0.049 is a unit-correction constant.

In systeme international units:

T=0.161 V/A

where V is the room cubic volume in m superscript 3, and A is the total absorption in the room figured with metric units.

The application of this equation can reveal some interesting things. Namely, double the sound absorption in the room while holding the room’s volume the same, and the reverberation time drops by half. Also, double the enclosed room’s volume, holding absorption unchanged, and you double the reverberation time. The reason for this is that in a bigger room, sound takes longer to be reflected from one absorbing surface to another. That seems simply a function of the longer sound-transit times between interactions with boundaries.

It is not quite that simple. Double the volume of a cube, and the distance from side to side (and thus the sound transit time) lengthens only 26%. Remember that we have doubled the volume while keeping the absorption the same. If the same total absorption were spread evenly over all the surfaces, it would only absorb 74% as much per unit area. Not only are the path lengths longer, but more reflections are also required for 60 dB attenuation of the reflected sound.

How sound is converted to heat

Where did that term A in the reverberation equation come from? What precisely does acoustic absorption mean? Read what Charles Dickens wrote in 1842:

Among the narrow thoroughfares at hand, there lingered, here and there, an ancient doorway of carved oak, from which, of old, the sounds of revelry and feasting often came; but now these mansions, only used for storehouses, were dark and dull and, being filled with wool and cotton and the like – such heavy merchandise as stifles sound and stops the throat of echo – had an air of palpable deadness about them which, added to their silence and desertion, made them very grim. (Dickens, 1844)

Dickens put it well: Wool, cotton and the like stifling sound and stopping the throat of echo. There it is, 150 years ago: Fuzzy stuff absorbs sound. It does so by being moved infinitesimally as the air molecules around it move.

Imagine waves rolling onto the seashore. They roll over damp, compacted sand without effect on it and continue rolling until their kinetic energy is exhausted. Now, imagine a hurricane has raised the seas, and the waves are rolling across a grassy lawn. Every time the waves ebb and flow, the blades of grass flop back and forth. The waves are now expending their kinetic energy by moving blades of grass, and under these circumstances, the same kinetic energy will not roll so far inland. (See Figure 2.)

If a door or window is at the room boundary with nothing beyond it to reflect sound back into the room, all sound falling on the open area will leave the room forever. This counts as acoustic absorption. Its absorptivity is an index of the rate at which it absorbs sound. An open window has an absorptivity of 1; all sound falling on it is absorbed. Its absorption is 1 times the open area.

If the area is calculated in square feet, this product is denominated in customary sabins. If the area is figured in square meters, this product is denoted in metric sabins. The sabin is the international unit of acoustic absorption, named after Sabine. Ordinary acoustic work will usually be conducted in all feet or all meters; whether the sabin is customary or metric is inferred from the context.

Fiberglass fuzz is highly absorptive, although it does not absorb quite all the sound. Its absorptivity is 0.8; that means 80% of the sound falling on it is absorbed. The absorption of its surface is 0.8 times the area exposed to the sound.

Brick, on the other hand, absorbs little and reflects most of the sound falling on it. Its absorptivity is 0.02, absorbing just 2% of the sound that strikes it. Thus, 98% of the sound that strikes brick is reflected back.

So far, we have covered only wall surfaces and finishes. Fully round objects in the room also absorb sound. A person standing away from near surfaces absorbs about 4.5 customary sabins (about 0.4 metric sabins). If the person were leaning against a wall, not so much absorbing surface would be exposed to the sound, so the absorption would be less. If the person were seated, the same would apply. When audience members in large spaces are seated, they are not counted as individual absorbers but rather as a surface area of a certain absorptivity. The absorptivity of an audience depends on the type of chairs they occupy and the percentage of chairs occupied when not all the chairs are full.

Absorptivity depends greatly on frequency because different materials absorb different amounts at different wavelengths. This is why absorptivities are ordinarily calculated quoted at a variety of frequencies.

Absorptivity of commercially available wall finishes also depends on the way the finish is mounted. Most absorbers work more efficiently at lower frequencies if an air space is behind them.

Sound distribution in architectural space

It will not surprise anyone who has attended an event in such a large space as an arena with a sound system that sound is not distributed evenly throughout the room. We have already considered sound distribution in time; it is now necessary to study the sound distribution in space.

We saw from the phenomenon of spreading losses that as we get farther away from the sound source, the sound coming directly from the source is at a correspondingly decreasing level. Something additional happens in a reverberant space: A reverberant field is created. This is sound of equal level throughout the space arriving from completely random directions and with a completely random phase relationship to the sound arriving directly from the sound source. In Figure 1, the reverberant field predominated from points F to G and from point G to point H; the decrease in sound level was the reverberant field dying away.

Imagine molasses being poured into a kitchen strainer. The fluid enters the strainer at one point but drips out over the entire bottom of the strainer. A dimple is at the point where the stream of molasses is introduced, but the surface is flatter from there to the edge of the strainer. This is something like the way sound distributes itself in a room: It enters at one point, the sound source, but it leaves by being absorbed through all the interior surfaces. The level is greatest near the source but much more uniform far away.

Figure 3 shows sound distributed in a reverberant room; the diagonal line shows spreading loss. If we are far enough away from the source for it to approximate a point source, this line will slant downward at 20 log x, a rate of -6 dB per doubling of distance. The horizontal line is the level of the reverberant field, constant at all distances in the room.

To calculate the level of this reverberant sound, in decibels relating to 20 mPa, you need to know L subscript w, the power level of the sound source in decibels relative to one picowatt (10 superscript -12 W). You also need to know the room volume in cubic feet (ft superscript 3) and the reverberation time. Use this formula:

L subscript w + 10 log (T/V) + 29.6

If the room volume is in m superscript 3, use this formula:

L subscript w + 10 log (T/V) + 19.3

Notice distance x from the source does not enter into these S equations because this level exists at all distances in the room.

To calculate the total sound-pressure level, direct sound plus reverberant sound, at any distance x we also need to know the directivity factor, Q, of the sound source. This is the formula using customary units:

L subscript w + 10 log (Q/4px superscript 2 + 81.6T/V) + 10.5

This is the formula using metric units:

L subscript w + 10 log (Q/4px superscript 2 + 24.8T/V) + 0.2

Where direct sound predominates, we get direct sound level; where reverberant sound predominates, we get reverberant sound level. Where direct and reverberant sound levels are equal, it will give the sum of the two, 3 dB higher than either.

When the power of the sound source is increased or decreased, both direct and reverberant levels increase by the same number of decibels. (See Figure 4.) The distances at which each predominate remains the same.

When the absorption in the room, and thus the reverberation time, changes, the reverberant level changes with it, whether increasing or decreasing. (See Figure 5.) The change in reverberant pressure level changes thus:

-10 log (A subscript 1 / A subscript 2)

This means that if the absorption doubles, -10 log 2 = -3 dB change, and if the absorption is reduced to 25%, -10 log 0.25 = +6 dB change.

When the directivity of the sound source changes, the distance at which direct sound and reverberant sound are equal changes. (See Figure 6.) This distance changes with the square root of the sound source’s directivity factor, Q. When the Q doubles, the distance at which direct sound and reverberant sound are equal moves away by 41%. For this distance to double, the Q must increase by a factor of 4.

The distribution of amplified sound in any venue obviously has much to do with the characteristics of the loudspeakers chosen, where the loudspeakers are placed and the direction in which they are aimed. In November, S&VC will cover the issues of sound out of doors and offer a number of sound reinforcement installation profiles that will illustrate the use of loudspeakers in real-life applications.

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