# Acoustics

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The concert hall is one of man's greatest joys; enjoying a fine symphony composed by the worlds greatest, performed by a world class orchestra. For months afterwards, the borgoise attendees will speak of the energy of the conductor, the orchestra responding to him, the power of it all. The crescendoes, the diminuendos, the stark silences between movements, the clarity of the soloist above the rest of the orchestra. Little do they know that were it not for the meticulous consideration of the architect at construction time, the patrons would not feel that they were getting their money's 'worth.'

The architect is tapping into the world of acoustics; in this case, achieving the best possible sonic experience through differing techniques : different materials, certain shapes of rooms, sound traps, etcetera. Acoustics and sound, like so many physics branches, starts out relatively simple and quickly becomes a gigantic headache. Massive amounts of planning must go into a large structure such as a concert hall, a dance hall. Even small structures, such as the phonebooth, have hours of careful planning put into their design, in order to achieve the desired effect with the varied sound sources. This page is designed to inform the reader in the basics of acoustics, using the theory behind acoustics and the examples of the concert hall and the dancehall.

Technically, the definition of 'sound' is a pressure wave in an elastic medium. This means that our pressure wave can be present in air, water, wood, steel... many different solids as well as air (and liquid). One of the most common units of measurement of sound is intensity, or the rate at which sound energy is being transmitted into the medium. (low sound intensity would be something like somebody clapping between movements, high sound intensity would be the applause after Beethoven's 9th) The unit of intensity is the decibel, or db. We use a logarithmic scale to measure these, as it is difficult to understand the range of the decibel in linear terms.

Other units of measurement are the period and the amplitude of the wave. As we see in the graphic, we have the graph of time versus sound pressure, with our little wave traversing it. The amplitude is the highest value the graph reaches before descending again, while the period is the amount of time it takes for the wave to complete a full cycle.

Other terms of note for the diagram are compression, which is represented by the parts of the graph in the positive region of sound pressure, and rarefraction, which is represented by negative pressure.

MLA Citation:
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### Popular Essays

Finally we have wavelength, which is the (distance traveled over one second) divided by (frequency). Knowing this size of the wave is incredibly important in designing rooms of all types.

The speed of sound, in fresh air, is 1130 feet per second. Other important data of note is that sound power can be represented by the equation

I = W / (4*(pi)*d^2)

Where I = sound intensity (watt/(cm^2)) W = sound power (watts), d = distance from sound source, (cm)
One should note that this is an inverse-square relationship between intensity and distance.Thus if the sound is a certain intensity at at a particular distance, if you go to twice that distance, the (perceived) sound intensity will be one quarter of its original intensity.

Suppose your living room is made completely of linoleum, for easy and quick cleanup. Suppose you are reading your favourite newspaper in the living room, while on the other side of the room a relative is watching the television. You will definately hear the sound waves of the TV that shoot directly from the TV to you, but you will also hear the sound waves of the TV bouncing off of the floor, the ceiling, all the walls, etcetera. Soon reading will become quite difficult as you are overwhelmed by the media.

If you had put acoustics into mind while building the house, perhaps you would have ended up with sound absorbant materials lining the ceiling and floors, ie acoustical ceiling tile and heavy carpet perhaps. Furthermore you would have lined the walls with heavy fabric curtains, heavily reducing the intensity of the waves that are reflected off those surfaces. Now, you have a pleasurable reading environment and a fashionable living space.

The materials that go into mind when building any room determine what kind of environment that room is going to be for noise. In some instances, you want sound to travel very far, such as a huge classroom with so many heads ready to learn. Other instances it is preferable for sound not to travel very far, such as the restuarant with many private conversations going on at once. Using ones knowledge of sound absorbtivity, one can create an optimal environment for every situation.

For entire rooms the equation a =(sigma) (S*b) is used, where a = total room absorption (sabins), S = surface area (ft^2) and b = sound absorption coefficient at a given frequency.
When a material absorbs sound, the sound energy is converted into heat energy.

The absorbtivity coefficient can range from 0 (no absorption) to 1, (complete absorption) although those extremes are incredibly rare, typically existing on in laboratory situations.
There are huge tables of sound absorption coefficients for all types of materials, but for our purposes we will only examine three.
Below is a table of absorption for one square foot of three different materials at 500hz.
Material
Open Window Plaster on 4" thick brick 1.5" thick fuzz
Sound Absorption 100% 2% 78%
Sabins (a) 1.0 0.02 0.78
Sound absorption Coefficent 1.0 0.02 0.78

Obviously, were we to have an area other than 1 square foot, the sabins and the coefficient would be different.
Important to note is that these are all the absorbtivity for 500Hz. Scientists and architects must be careful to consider all frequencies, architects especially, because they may neglect certain frequencies in favor of the desired effect with others. For instance, in restaurant settings, architects are primarily concerned with the midrange frequencies of human speech. Concert hall architects are not so lucky.

Typically materials having coefficients larger than 0.20 are considered "Sound-absorbing" while materials with coefficients under 0.20 are "sound-reflecting." A difference in about 0.10-0.20 is considered a significant effect on sound absorbancy, while anything above 0.20 is a considerable amount of change.

Reverberation Time

The work of Wallace Clement Sabine (for which the sabin is named) includes the investigation of Reverberation time, or how long sounds persist in a room. He was inspired by Harvard's lecture all in the Fogg Art Museum, as sound echoes would persist for 5.5 seconds after they were emitted. He chose to use an organ pipe in the hall in the middle of the night, when ambient noise was the quietist, and would emit a 512hz tone at 60dB to see how long the sound would persist. Eventually he found that he could lower the reverberation time using seat cushions from a nearby theatre and placing them on the walls. Eventually he found that

T = 0.05(V / a)

where T = reverberation time (seconds), V = room volume, cu ft), and a = total room absorption (sabins)

Different reverberation times are desired for different effects. A large reverberation time gives the sense of something very large and grand, thus cathedrals and many symphonic works desire something of a high reverberation time. (1.6 to 2.0 seconds, or even greater in cathedral settings) Our restaurant, however, will most likely be popular if it has a low reverberation time, somewhere around 0.6 to 0.8 seconds.

Now that we have an idea of how materials effect the intensity and reverberation time of sounds in a room, we can move onto room acoustics.

The Greeks had the idea, way back in the day. They placed their theatres on steep hillsides and quiet rural locations, trying to avoid gusty winds as well as urban noise. The circular seating plan allowed more of the audience to be closer to the stage, the actors. Raising the seats in the back allowed all the audience to hear the actors with increased clarity than before. Still this can be improved upon heavily using up-to-date production techniques.

There are three basic uses of the reflectivity of sound in a room acoustics environment :

*

Reflection : Reflection is obviously the return of a sound wave from a surface. If the surface is large compared with the wavelength of the sound, then the angle of the reflected wave will equal the original angle of incidence. For example, we have a sound wave of say 1000Hz and our wall is 4 feet long. 1000Hz corresponds to a wavelength of about 1 ft, so a 4ft long wall will easily reflect the given sound wave (and any with frequencies higher than 1000hz, for their wavelengths grow smaller the larger the frequency)

*

Diffusion : Diffusion occurs when the wavelength is equal to the surface that reflects it. Diffusion is the scattering of a sound wave from a surface. Typically surfaces will make up a continuous surface, but will connect with each other at shallow angles to 'break up' sound evenly. This is optimal when there is a large area of sound producers and you want each one to sound amongst the others in all corners of the room. Whereas if you have a single performer an angled reflective surface will be most useful.

*

Diffraction : Diffraction is the bending of a sound around an object. This occurs when the reflecting surface is smaller than the wavelength of the reflected wave. Typically these surfaces will be spaced out so that some of the sound goes 'through' them.

After these, angles and the dreaded trigonometry come into play. A flat reflector huge from the ceiling with no angle will simply reflect sound waves evenly to an entire audience, which is nice, but can be improved upon. If we were to angle the reflector at a convex angle (to the perspective of the speaker) then the sound energy is distributed for a better listening experience for those in the back. The converse of this example, were we to have a concave reflector, would focus sound energy on a specific area, which would not be good for people outside said area and would cause echoes as well.

A rough way of finding if a room will echo or not is using a ray-diagram analysis. By charting sound wave rays from speaker to listener in key points around the room, one will be able to tell if a room will have a strong echo or not.

We have the direct line-of-sight sound wave ray for each listener, 12ft and 33ft. Then we have the reflected rays, which add up to a distance of (11+18 = 29ft) and (16 + 26 = 42 ft). If we find the difference of these numbers, they end up being 17ft for the closer person, and 9 ft for the far away person. We then apply those numbers to a table of sound-path difference, and we see if the 'echoes' produced are small enough that they may be neglected.

Since our largest number is 17ft, we are under 28 and excellent for speech.This particular example only works for situations where there is one origin of noise - in multiple origin contexts, such as a meeting/board room, the entire room must be optomized for participants to be able to hear a speaker from anywhere in the room Or for our dance club, where speakers are placed everywhere in the room.

the lovely Davis concert hall. This hall is used as an example of acoustics at work in a concert hall.

At first glance one can note the concave reflector at the top, although for some reason it is broken up at various points for lights to hang down from. There is enough surface area up there, however, that the reflector works in reflecting most of the sound sent from the stage. Also note the walls behind the stage - they are recessed squares, each containing a V-shaped backing. Interestingly the walls alternate by either having a convex or a concave backing. Assumedly this is for maximum diffusion of sounds so that no one position in the theatre is the focal point of reflected sound. The walls of the theatre, although you cannot see them, are designed mainly to dissipate sound - the walls are made of sound absorbant material comparable to carpet.

It is the opinion of the author that this hall was designed with fashion in mind more than pure acoustics. Were the author to revise the theatre, he would improve the reflector at the top of the theatre by decreasing the gaps provided for lights. He would then angle the walls of the theatre (those walls not visible in the picture) to diffuse the sound rather than absorb it - he would most likely use sound-reflecting materials with a high coefficient of absorption, as he doesn't want all the sound reflected back at the audience. He would also angle these diffusional wall down slightly, that the reflected sound is not reflected up into the ceiling where there is no reflector and no audience. These are the revisions of a physics 211x student.

Now, to design our own concert hall.

We have chosen the original Greek design of a stage surrounded in a semi-circle by the audience. Since this hall will be used primarily to host speeches by politico revolutionairies and the author's beer bottle quartet, a large stage is not needed. And since we will have a rather large audience at each concert, we will need quite a bit of sound reflected to the back. We have chosen a semi-circular backdrop behind the performers, angled in such a way that it will diffuse the soundwaves.

At right we have the performers on the stage. Sound waves will travel directly from performer to listener, but the clanging of the sticks upon bottles will also travel into the shell and be reflected and diffused in the direction of the audience. We use a diffusionary wall design in order to minimize any 'sweet spots' in the theatre, rather, the entire theatre is the sweet spot.

At left we have our theatre design, note the angled ceiling in order to provide the rear audience with the most sound possible. The audience near the stage is receiving plenty of noise already. The walls of this hall will be designed to have a rather low reverberation time, as the percussive beer bottle group's sound will not be enhanced by a long reverberation, nor will speech. Thus the walls will be constructed of a material with a rather high absorbacy coefficient (0.40) and will be angled to diffuse the sound evenly throughout the theatre.

The colour scheme of this theatre will be lime green and hot pink, designed to have the audience close their eyes to avoid the terrible visuals. This will increase their reliance upon their ears and overall will produce an even more intense sonic experience.

Now, onto the dance club...

Creating a good dance club is quite different from the concert hall.
As before we wanted an even distribution of sound, but we do not have the good fortune of being able to have a sloped floor (without the dancers falling on their behinds). Much of what goes into creating a most excellent dancefloor is up to the sound engineer, who decides what speakers go where. Yet, an architect can do what he can to make life easiest for the engineer.

With many concert halls, a long reverberation time is preferred, as it enhances the sound of the orchestra - in this setting, we want a rather low reverberation time - no more than 1.2 seconds. Thus we will put heavy curtains on the walls to absorb as much of the sound as possible. The ceiling will also be absorbant - we will hang a sound diffracting mesh from the ceiling, and the real ceiling will be a highly absorbant foam core. We use the mesh as a first level diffuser, but for the most part we are doing it for aesthetics, and also to provide a solid base for the light guys to do their thing.

The room will be something of a parallelogram, and we need not worry about the stage for the speakers placed throughout the room will be making the sound, not the dj. The dancefloor we need not worry about either, for it will be covered with people and they absorb most of the sound before it hits the floor. For their comfort it is suggested that a thick wood floor is used, or perhaps a very very light carpet? We will consult a dance expert.

After that it's up to the sound engineer to make our club come to life.