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.

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.

Room Acoustics!