Room Acoustics & Reverberation Time RT(60)

  • kyriakos

    kyriakos

    Administrator

    Information about this interesting subject is collected from here and there (from the old phpBB Forum and the AVSite Forum) and also I have designed an excel model (just for fun... )

    **Definitions:**

    Reverberation:
    Is the persistence of sound in a particular space, after the original sound is removed. When sound is produced in a space, a large number of echoes build up and then slowly fade out. This process of damping is because the sound is absorbed by the walls, the floor, the ceiling and the air.
    Large chambers, like cathedrals, churches etc., are examples of spaces where the reverberation time is long and often can clearly be heard. The stony walls, floors and ceilings of those halls don't damp the sound so that the reflections can move around for a very long time. Nevertheless the high frequencies fade out first so the reverb becomes darker and darker the longer it "exists".

    Direct Sound:
    This is the sound which receives you on the direct way without any reflection.

    Early Reflections:
    Some milliseconds after you heard the direct sound the first reflected waves arrive your ears: Early Reflections. Our brain "gives" us an impression of the room size with these Early Reflections. These delays normally are in a range from 5ms to 30, ... 50ms. By the way: The sound needs around 3ms to "travel" 1m through the air.

    Reverb:
    More and more we recognize reflections - from the walls, the ceiling, the floor and from objects in the room. The sum of all these reflections we call reverberation > "Reverb"

    **Introductory:**

    W. C. Sabine carried out a considerable amount of research in acoustics and arrived at an empirical relationship between the volume of an auditorium, the amount of absorptive material within it and a quantity which he called the Reverberation Time (RT).
    As defined by Sabine, the RT(60) is the time taken for a continuous sound within a room to decay by 60 dB (one million times) after being abruptly switched off. The absorption coefficient of any material, as originally defined by W. Sabine, is the ratio of the sound absorbed by that material to that absorbed by an equivalent area of open window.

    Thus a perfectly absorbent material would have an absorption coefficient of 1 and an absorption unit of 1 Sabine represents a surface capable of absorbing sound at the same rate as 1m² of open window. Using a simple formula, and providing one knows the surface areas and absorption coefficients of the materials to be used, the reverberation time of a room can be determined at the design stage.

    **Theory:**

    Just for a general room acoustics scan-study, read this: link and this:

    link (5 pages in Greek)

    The basic formula for calculating the RT(60) for closed rooms and uniformly distributed absorption in the room is the one produced by Wallace Sabine: (link )

    RT(60) = 55.25 * V / (c * A) = 0.161 * V / A

    Where:

    • RT(60) – Time for a 60db sound absorption (sec),
    • V = Volume of the room (cu.m.),
    • c = The speed of sound in the air (343 m./sec),
    • A = Absorption (for a specific frequency) of the room (Sabins). A is calculated as the sum of the multiplications of the various material surfaces times the absorption coefficient "s": [A = (a1 x s1) + (a2 x s2) +...].

    Or in feet: RT(60) = 0.049 * V / A

    In case of non uniformly distributed absorption in a closed room the modified Fitzroy equation is used. (link )

    For large closed spaces such as Auditoriums and Music Halls, the Sabine equation becomes:

    RT(60) = 0.161 * V / A + X * V (X = absorption coefficient of the air).

    Here is another equation:

    G = 13.8 * V / [4 * pi * c * d² * RT(60)]

    Where:

    • G = the direct/reflected sound ratio,
    • V = Volume of the room (cu.m.),
    • d = Listening distance (m.),
    • pi = 3.14159... and
    • c = The speed of sound in the air (343 m./sec)

    or to put it simpler: 1/G = 313.24 * d² * RT(60) / V

    They say that a nice figure of RT(60) for our listening rooms is 0.70 sec. Larger than that is good for classical music and lower than that is better for Jazz and human voice reproduction. The graphs on the right can also be used (taken from link ).

    The equations above are used for educational and historical purposes and their application in a typical listening room will not give an accurate picture of the real world. Nowadays sophisticated PC programs are used in order to measure the RT(60) of a space at the listener's position.

    Simple calculations can be performed on line, using java:
    - link
    - link
    - link (room mode calculator)

    For a deeper and more sophisticated approach, I have found the 2 websites below, where PC programs must be purchased and downloaded:
    - link
    - link

    As a reference, if you want to elaborate further, read the: Introduction to Acoustics, by Prof. R. D. Ford (Publisher: Elsevier)

    to be continued...

    1  16 Sep 2010  
  • Trouble

    Trouble

    ACA Member

    To be continued where? In Dr. Ford's introduction to acoustics? Or here where you will take this all the way to heaven?

    2  16 Sep 2010  
  • Trouble

    Trouble

    ACA Member

    I read this article ten times to finally understand it.

    I am sure our tech boys will get it all within minutes, but for someone who does not take math to the max, it takes time to fully comprehend.

    3  16 Sep 2010  
  • kyriakos

    kyriakos

    Administrator

    Comparing, using a model...

    I have designed an excel sheet (model), putting the absorption coefficients of the most common material over certain frequencies and applying the simple formulas above, it gives an estimation of what the reverberation curve would look like. Following are just some examples to see if it works...

    Example#1:

    Let's try to justify why we prefer to put carpets and curtains and furniture in our room, for quality listening... (Most of the times it works and you don't need to put any extra exotic materials...). Let's assume a small to medium room of 28 sq. m, with a marble floor:

    1. In the room there is only one listening seat and one person. No furniture, no carpets, no curtains nothing. Some glass windows are assumed. The result of the reverberation curve will be something like that:
    RT(60) average=2.62, Reflected/Direct Sound Ratio=57.84 @ 2.33m. listening distance.

    2. The same room has a carpet (55% of the floor) and curtains (to cover most of the glass) with still one listening seat and one person. The result of the reverberation curve will be something like that:
    RT(60) average=1.14, Reflected/Direct Sound Ratio=25.11 @ 2.33m. listening distance.

    3. The same room has a carpet and curtains and furniture this time (like libraries on the wall and wooden furniture on the floor), with 3 heavy seats and still one person. The result of the reverberation curve will be something like that:
    RT(60) average=1.02, Reflected/Direct Sound Ratio=22.51 @ 2.33m. listening distance.

    4. The same room as above with 11 persons as well (max allowed according to a rule of thumb). The result of the reverberation curve will be something like that:
    RT(60) average=0.78, Reflected/Direct Sound Ratio=17.3 @ 2.33m. listening distance.

    Example#2:

    Let's try a similar comparison in a larger room (I would call it an average listening room) 9.6 x 5.3 x 2.95m. (LxWxH), with a 90% thick carpet coverage (rest is furniture, case 1) and no carpets at all (case 2), with a listening seat set @ 2.8m.:

    1. RT(60) average=1.08, Reflected/Direct Sound Ratio=17.50

    2. RT(60) average=1.73, Reflected/Direct Sound Ratio=28.12.

    Example#3:

    Something that is very essential to our listening satisfaction is the fact that in our rooms the reflected/direct sound ratio is very much larger than the ratio in a Concert Hall, which is something like 5 to 25, depending on the listening distance from the center of the orchestra.

    See what's happening in a living room 9.6 x 5.3 x 2.95m. (LxWxH), at listening distances of 2m. and 4m. from the speakers respectively:
    Doubling the listening distance, the direct sound (energy) gets 4 times less (not applicable for line array speakers...), although the reflected sound energy remains almost constant, so the ratio 1/G goes 4 times larger (from 10 and 40!)

    The studies of Zahorik & Wightman (2001) and Zahorik (2002) have analyzed the above:

    See now what's happening with the reverberation curve in an auditorium (@ 12 m. listening distance), how "smoother" things are (smaller inclination of the reverberation curve and less the dispersion from the mean value for the different frequencies).

    By the way, take a look at the following:
    - link
    - link
    - link
    - link

    Example#4:

    Just to play a bit further, please compare the value of RT(60) and 1/G in the above auditorium with audience coverage of 99% and with audience coverage of 1%. This is also happening at home, if we listen with many people sitting and with no people in the room.

    The above graphs and excel sheets and models and everything can only give an idea, if terrible things are happening in your listening room as far as reverberation time, ambiance and this sort of thing... The curves of the measurements shown are nearly textbook perfect, but in real life you often get "peaky", irregular shaped curves under the 100 Hz and towards the 20 Hz due to comb effect. They say NOTHING and DO NOT distinguish rooms that have parallel or nonparallel walls for example, which makes a hell of a lot of difference in listening, as you understand...

    I would comment that according to those graphs, we could put any kind of acoustic material in his room, make the graphs really look straight and horizontal but still the room would remain acoustically HELL! And this is simply because this excel model says nothing about room dimensions and dimension ratios...

    But it is not supposed to deal with that... There are civil engineers out there, who can build a better room for you...

    Additional comments:

    It has been proved by studies and experiments that the sound absorption coefficient and the Sabin units calculated for a given area, may be dramatically increased when the material is distributed on four different surfaces, in comparison with the coating on a single surface of that area. The fact is attributed to rim diffraction phenomena, connected with the increased of free edges of the material, resulting to a more extensive pseudo-coverage than the actual one.

    This phenomenon also depends on the considered frequency. It is more evident at frequencies around 2000 Hz, minimizing at 700 and 8000 Hz of the frequency spectrum. The application however of the absorbent material so that it has areas of discontinuity, disperses the sound fronts, leading to an improvement of the diffusion field. Arches and concave surfaces are not desirable in the listening rooms, acting as acoustic "lenses" that focus the sound energy in specific locations, instead of spreading it out. This focus phenomenon is minimized as the curvature of the surface tends to level off.

    On the contrary, convex cylindrical surfaces of plywood or MDF etc have the opposite effect on the incident sound waves. Apart from the dispersible reflection, part of the sound energy may be absorbed (depending on composition), or even being re-emitted through stimulation of semi-cylindrical baffles within the listening room. A flat diaphragm would send the sound radiation at an angle range of 20 degrees in comparison to an equivalent cylindrical diaphragm, which has corresponding angles of sound radiation at around 120 degrees.

    - link

    This triple action is better achieved with the form of successive vertical semi-cylindrical sections to improve the acoustic behaviour of a room at low frequency components, calculated through a combination of absorbing and dissipating sound energy. Necessary conditions for their successful implementation are to have dimensions comparable to the wavelengths of sound which we want to disperse, and the asymmetrical arrangement of these cylinders within the study area.

    The irregular structure reduces the possibility of the notched diffraction side effect and the resulting selective enhancement of specific frequencies - something that runs counter to the desired properties of a diffuser. The axes of symmetry of multi-cylinder encompassing groupings in different areas of the room must be vertical. The application of planar polygonal scattered clusters is less effective than the ones of poly-cylindrical section.

    -

    4  16 Sep 2010  
  • kyriakos

    kyriakos

    Administrator

    Trouble wrote:
    To be continued where? In Dr. Ford's introduction to acoustics? Or here where you will take this all the way to heaven?

    Tony, I think room acoustics is the most important factor in our music reproduction, something that sometimes we put aside... Then comes... the speaker...

    Sorry for all that maths, I just wanted to point out that those formulas have not been produced from outer space...

    5  16 Sep 2010  
  • Trouble

    Trouble

    ACA Member

    They don't look like they r from outer space, but I wonder if anyone really does the math on there system?

    6  16 Sep 2010  
  • Mikekan

    Mikekan

    ACA Member

    Please continue at the white papers section. Tony lock it if you want.

    7  16 Sep 2010  
  • Trouble

    Trouble

    ACA Member

    Its okay, we can keep it open in case others want to work backwards...

    8  16 Sep 2010  
  • gherop

    gherop

    ACA Member

    Excellent article.
    These kind of articles are very important for our Club.
    They are towards a better understanding of why we think that we like or dislike a system.
    Poor Hi-End systems, only if you knew how little contribution you have to music (sound) satisfaction, when compared with room acoustics...

    9  17 Sep 2010  
  • Trouble

    Trouble

    ACA Member

    I totally agree.

    White papers in general should be our holy grail to Audiophile Anonymous as us.

    10  17 Sep 2010  
  • kyriakos

    kyriakos

    Administrator

    gherop wrote:
    Excellent article.
    These kind of articles are very important for our Club.
    They are towards a better understanding of why we think that we like or dislike a system.
    Poor Hi-End systems, only if you knew how little contribution you have to music (sound) satisfaction, when compared with room acoustics...

    Thank you George !

    11  17 Sep 2010  
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