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Natural Science Forum / Physics / Acoustics / February 2004Basic acoustic properties calculator
Newbie posting... In order to develop my own understanding of basic room acoustics, I have put together this Excel spread sheet that will calculate various useful values about the acoustic properties of a rectilinear room. http://216.12.218.129/members/ChrisW/Control%20Room%20Calculator.xls For those with the time, inclination and expertise, I would appreciate some constructive feedback as to the accuracy and usefulness of such a spreadsheet. The spreadsheet provides the following: o RT60 values according to Sabine, Eyring and Fitzroy's equations o Allows you to choose from a reasonably wide range of wall, floor and ceiling materials o Allows you to choose room dimensions that are in ratios favourable for good modal distribution, or some user defined ratios o Graph showing "On axis" absorption as used by Fitzroy's equation. This is helpful for showing uneven distribution of absorbancy and eliminating a possible source of flutter echo o The number and spacing of modes below a user defined cutoff o Mean free path o Schroeder transition frequency o Schroeder diffuser calculator NB: I have seen Fitzroy's equation quoted with an initial multiplicand that ranges from 0.16 to 0.163 in value. I have used the value of 0.163 as quoted by Reinhard Neubauer in his paper from ISSEM'99 in Gdansk. On the resonant modes sheet, since the simple graph of the first 200 modes does not indicate which order the mode belongs to, it presents a possibly misleading impression. Therefore, I would like to implement another graph that shows the net contribution each mode makes to the overall field - but I can't find the equations to show me how to do this... Any assistance here would be gratefully received. I also wanted to implement Kuttruff's correction to Fitzroy's equation that implements an effective absorption coefficient (alpha *) to take into account unequal absorption distribution within a single surface; but this proved more complex to do than Neubauer's papers let on - so I scrapped that stuff. Thanks Chris Whealy  SignatureThe voice of ignorance speaks loud and long, but the words of the wise are quiet and few. -- Chris, I haven't checked it through but it looks really nice. However I really believe it's important that you CLEARLY state all sources and links. Credit where credit is due !!!!! I see you use Temperatures (a bit far fetched, but fun to see the effect) to calculate velocity. I should advice to use the formulas below, which are also integrated in ASTM C 423. They are rather accurate formula and also often used in Europe. However in the 1985 edition of ISO 354 I have c is defined as: c= 331 + (0.6 * T°C) I don't know if this is changed in a later addition. You use 331.5+(0.61*T°C) Your question marks about those factors 0.16 to 0.163. They are ALL correct but since they are temperature dependent (in fact velocity dependent), and since you use Temperature anyhow you can as well correct this factor 0.161 with the temperature. The formulas you can find below. I never saw any standard or norm explaining the origin of this Factor 0.16 to 0.163. This Factor is Temperature related and are all correct. So here's the formula: Factor = 60/(c*(10*log(exp(1))/4)) = 24/(c*log(exp(1))) c = velocity of sound in air c = 20.047*sqrt(K) = 20.047*sqrt(273.15 + T°C) [m/sec] c = 49.022*sqrt(K) = 49.022*sqrt(459.67 + T°F) [ft/sec] Factor 0.16 = 285.92 K = 23.6850 °C = 74.6330 °F Factor 0.161 = 293.07 K = 20.0091 °C = 68.0164 °F Factor 0.163 = 293.07 K = 12.8591 °C = 55.1464 °F In fact the 0.161 factor seems the most logical and is used in many standards. ASTM C423 (reverb room absorption) integrates this temperature calculates as per the above formulae: A = 0.9210*Vd/c where: A = sound absorption, m2 or Sab, V = volume of reverberation room, m3 or ft3, c = speed of sound (calculated according to the 20.047 * .....), m/s or ft/s, and d = decay rate, dB/s, For the others: related to the previous discussion about A versus Sabines. ASTM 423 (American) itself uses A !!!! Angelo: Maybe The Americans themselves are jealous of their own Sabine? Just a joke (couldn't leave it - just teasing). Note that you as well can adjust this factor 0.163 in the standard Sabine formula in function of Temperature/Velocity. Please respect sources and links. If you make something, distinguish between your work and other's. Also tell where the absorption values come from. Eric www.acoustics-noise.com > Newbie posting... > [quoted text clipped - 44 lines] > > Chris Whealy Chris, I forgot: It should be good if you allow to enter all parameters in Imperial units too! For that you don't have to adjust all formulas (otherwise file becomes to complicated). Just convert those Imperial input values to Metric and vice versa for output. Allow the user with a push button or checkbox or option buttons to define the type of units: Metric or Imperial. Kind regards Eric > Chris, > [quoted text clipped - 111 lines] > > > > Chris Whealy Sorry, Forgot to correct the Kelvins: Was: > Factor 0.16 = 285.92 K = 23.6850 °C = 74.6330 °F > Factor 0.161 = 293.07 K = 20.0091 °C = 68.0164 °F > Factor 0.163 = 293.07 K = 12.8591 °C = 55.1464 °F Must be: Factor 0.16 = 296.8350 K = 534.3030 R = 23.6850 °C = 74.6330 °F Factor 0.161 = 293.1591 K = 527.6864 R = 20.0091 °C = 68.0164 °F Factor 0.163 = 286.0091 K = 514.8164 R = 12.8591 °C = 55.1464 °F K: Kelvin R: Rankine C: Celsius F Farenheit Eric www.acoustics-noise.com > Chris, > > I haven't checked it through but it looks really nice. > However I really believe it's important that you CLEARLY state all sources > and links. > Credit where credit is due !!!!! <snip> Wow! Thanks for the comprehensive answer! You've given me alot more work, but hey, I appreciate the fact that you've taken the time to review my work. Thanks alot! As for my sources, I'll have to dig around and remember where I got the information from. Most of it is from F.Alton Everest, Reinhard Neubauer (Ingolstadt, Germany), Dr Y.W. Lam (University of Salford, UK) and many others. I'll add a credits and references sheet with weblinks where applicable. As for the air temperature stuff, I'll adjust the formula as per your recommendations. I'll correct the factor in Fitzroy's equation to 0.16 and implement a metric/imperial option. I have also successfully implemented Neubauer's correction to Fitzroy using Kuttruff's "effective absorption coefficient". I've also thrown in Arau's formula just for comparison. One other thing that I have implemented now is mode attenuation because I wanted to show the contribution each mode made to the overall field. The formula was derived from Dr Lam's paper on diffuse field room acoustics and calculates the attenuation as (1-alpha)^N where N is number of reflections. I have added this plot to the resonant modes plot, but I'd like your opinion on whether it shows anything useful or not. I'll mail you the spreadsheet seperately. Thanks Chris SignatureThe voice of ignorance speaks loud and long, but the words of the wise are quiet and few. -- Hello Chris, I like your response, and willingness to introduce sources. 1) Too much is available on the net where people take credit for others work. 2) If you really want to help others and to share it's very good that they find the links to the original documents, in order to get a better understanding what your file and they themselves are doing. But there are also practical reasons. E.g. The edge effect (diffraction) on ASTM absorption measurements is larger than on ISO measurements. Etc. Why do you only refer to Fitzroy in relation to this factor 0.16 ? This is as well valid for Sabine and Eyring. And I should prefer 0.161 rather than 0.16 which is more logical for inside temperatures. And this 0.161 is used in many standards too. I'll have a look to your newly adjusted file, but please give me time (it's not that one can analyse this in a few minutes). I think it can also be useful that you look at my room mode calculator Excel file on my site. In the Help page there are also links to related documents. and references to Authors. Indeed for modes it is important to distinguish between the different types of modes. It should be nice if you go more in-depth on the Higini ARAU approach. This is very difficult to find on the net. I really do like his approach , and DO respect him enormously (as scientist and person). I think Arau's disadvantage is that he mainly publishes in Spanish (his country) and that he is too honest to put his, in Acta Acustica published method on the net (article which is not easy to get by). Kind regards Eric > > Chris, > > [quoted text clipped - 36 lines] > > Chris Correction, I better should do it correct the first time (less bandwidth, better oversight, less time) :):):) Why do you refer to a constant factor? If you use Temp. to influence velocity (which is not directly that important but mainly fun) than don't use a constant but define this factor in function of c which depends on T. Or did I misunderstood? Eric > Hello Chris, > [quoted text clipped - 3 lines] > temperatures. > And this 0.161 is used in many standards too. > Hello Chris, ..snip... > Why do you only refer to Fitzroy in relation to this factor 0.16 ? > This is as well valid for Sabine and Eyring. > And I should prefer 0.161 rather than 0.16 which is more logical for inside > temperatures. > And this 0.161 is used in many standards too. ...snip... 0.161 may signal to users that the accuracy of estimated quantities, like reverberation time, is 1/1000 s (= the third decimal is significant). Of cource, if expected by a standard, we have to use this accurate number, if we make something "in accordance with" the standard. Usually the mean free path length is a much more inaccurate quantity than the speed of sound, c. Using a more accurate sound speed value (at temperature t) do not necessarily increase, e.g., the accuracy of estimated reverberation time, T60 dB. Actually, the mean free path length is not an unique quantity (as is c in air in certain temperature) at all. Have a look at Joyce W B, Sabine's reverberation time and ergodic auditoriums J. Acoust. Soc. Am, 58(1975)3, 643 - 655, + corrections in 59:1, p. 234. Kari Pesonen > Hello Chris, > > I like your response, and willingness to introduce sources. :-) > 1) Too much is available on the net where people take credit for others > work. True. I dare say that some of the sources I have quoted are "borrowing" information from others. This is why I have made the comment that certain sources I have cited may not necessarily be the primary source. > 2) If you really want to help others and to share it's very good that they > find the links to the original documents, in order to get a better > understanding what your file and they themselves are doing. Where know, I have put in hypertext links for all web sources > Why do you only refer to Fitzroy in relation to this factor 0.16 ? > This is as well valid for Sabine and Eyring. Corrected > I'll have a look to your newly adjusted file, but please give me time (it's > not that one can analyse this in a few minutes). Before you do that, please mail me for the most up-to-date spreadsheet. I've spent a long time working on this spreadsheet, and I don't have time to make any further changes. So this version is the last - I promise! Please mail me with the format you require. I have versions for Microsoft Office XP, Excel 97 or Excel 95. Also StarOffice 7 and StarCalc 5. Unfortunately, my free webspace has just died, so I will have to mail people copies on request. Don't be shy now! > I think it can also be useful that you look at my room mode calculator Excel > file on my site. > In the Help page there are also links to related documents. and references > to Authors. I will certainly take a look. > Indeed for modes it is important to distinguish between the different types > of modes. Does the plot of mode attenuation show anything useful? > It should be nice if you go more in-depth on the Higini ARAU approach. I'd love to, but I don't have the time. > This is very difficult to find on the net. Tell me about it! Thanks for your input. I will cross post the availability of this spreadsheet to rec.audio.pro and rec.audio.tech. Chris Whealy SignatureThe voice of ignorance speaks loud and long, but the words of the wise are quiet and few. -- There is now a small web page from which this spreadsheet can be downloaded. The previously quoted link has been removed. http://www.rmmpnet.org/members/ChrisW/index.html Any objective feedback would be welcome. Chris W SignatureThe voice of ignorance speaks loud and long, but the words of the wise are quiet and few. -- > There is now a small web page from which this spreadsheet can be > downloaded. The previously quoted link has been removed. > http://www.rmmpnet.org/members/ChrisW/index.html > Any objective feedback would be welcome. I must say that, after a brief sojourn through this spreadsheet, I am impressed with the thoroughness of this room acoustics treatment. I must also say that after years of exposure to the "control room" acoustics enigma, I have yet to be impressed by any gravity in the problem, not to say that there is not a great deal of same. The enigma seems (to me) to be woven into the ultimate desires of the mixing technicians, where they demand that the aural space in which they practice must also represent that of the ultimate listeners, in their space. Here is where some confusion might arise in he wider professional communities (architects, Engineers, lawyers, owners, consultants in general) in that the space is thus no longer just a small work-space; rather it has become an important audition space where media sound quality undergoes its final adjustment and quality control judgment; hardly just a "control room". It is important that the audio industry make this distinction in its promulgation of the design concepts for and construction of same. Chris's spreadsheet treatise provides a valuable missing link in this quest; a quantitative tool that can technically represent the technician's audition space! The next step (if I may) in this process is to model the space(s) of the ultimate media consumer-listeners. Such final spaces generally may be small, or large, or dry, or reverberant. It "would be nice if" one could even supply variable acoustics to this control-room-audition space so that the end result of the mixing can be graded instantly by a trained, or not-so-trained listener-judges. One manner in which this particular need is now being fulfilled in part is by the "auralization" community. Lest they steal your (control-room-audition folks') thunder, Chris's work needs to be soon extended in that (variable acoustics) direction... my 2 cents.... Angelo Campanella Signature--------- www.CampanellaAcoustics.com --------- "I have simply studied carefully whatever I've undertaken, and tried to hold a reserve that would carry me through." - Charles A. Lindbergh. "As for background noise level; 35 dBA is a good classroom; 45 dBA is a sound masking system!" - Anthony K. Hoover >> There is now a small web page from which this spreadsheet can be >> downloaded. The previously quoted link has been removed. >> http://www.rmmpnet.org/members/ChrisW/index.html >> Any objective feedback would be welcome. After a second look, I am not clear on the third worksheet (Resonant Modes). I would expect that the top graph would be a room response for constant inout of some sort, vs frequency being the horizontal (x-) axis. However instead I see frequency on the Y- axis, and that the first mode would be of the lowest frequency. Can you explain the facts and significance of the top rgaph ("Resonant Frequenciesand their Attenuation")? Angelo Campanella > After a second look, I am not clear on the third worksheet (Resonant > Modes). I would expect that the top graph would be a room response for [quoted text clipped - 4 lines] > > Angelo Campanella Hi Angelo, First of all, thank you for the complementary review. I have tried to make the results as objective as possible! The RT60 values turned out by my spreadsheet are only in relation to an *empty* room in which the wall, floor and ceiling surfaces are of the stated absorbancy. If you want to "hear" the results of variable acoustics, then what you're really asking for is some form of "dynamic auralisation". As I understand it, it is beyond the current capability of the average PC to modify an anechoic sound file "on-the-fly". Even CATT Acoustic http://www.catt.se takes a staged approach to auralisation. Output files must first be calculated to describe the sound field at a given listener position, and then these are fed into the auraliser processor. This is a batch process, not an online one. Unfortunately, I think it is beyond Excel's capability to deliver the next required step. As for the Attenuation plot on the Resonant Modes sheet, this was a first attempt at modelling the contribution each mode makes to the overal sound field. However, all that is plotted is the level of attenuation experienced by a mode after it has been reflected off N surfaces (where N is the mode order). This is calculated using a formula I found in a paper by Prof Y.W. Lam (then Dr) of the University of Salford, UK. http://www.acoustics.salford.ac.uk/student_area/bsc3/room_acoustics/DiffuseField %20&%20Parameters%202003.pdf What is plotted is (x_axis_rho^N)*(y_axis_rho^N)*(z_axis_rho^N), where N is the mode order and ?_axis_rho is the on-axis reflectivity in a given direction. This gives the overall level of attenuation for a mode of a given order, but not the direct effect it has on the SPL of that mode in a field of a particular strength. If there is a better way of showing mode contribution to the overall field, then please let me know. Regards Chris W > The RT60 values turned out by my spreadsheet are only in relation to > an *empty* room in which the wall, floor and ceiling surfaces are of > the stated absorbancy. If you want to "hear" the results of variable > acoustics, then what you're really asking for is some form of "dynamic > auralisation". As I understand it, it is beyond the current > capability of the average PC to modify an anechoic sound file > "on-the-fly". Even CATT Acoustic http://www.catt.se takes a staged It is not absolutely necessary at this time to "hear" the results (but it "would be nice" some day). > As for the Attenuation plot on the Resonant Modes sheet, this was a > first attempt at modelling the contribution each mode makes to the > overal sound field. However, all that is plotted is the level of > attenuation experienced by a mode after it has been reflected off N Theorizing is a fascinating indoor sport, but in architectural design, we need proven (empirical included) real world formulations. The next step should be to take real world data in a room of that size, with known surfaces, e.g. an available classroom, office or control room.What is missing at the moment is a good paradigm for audition spaces (aka "control rooms"). Beranek has done this in spades for music halls. Your audition space Works (for the lack of a better term) should be a summary of results of personal evluations of such spaces along with physical measurements that are RT60, C80, D50 EDT, even G. I have some preliminary data on such spaces as meeting rooms, but the results so far are varied, and lack the rendered judgement of "suitability for audition". Angelo Campanella --------- www.CampanellaAcoustics.com --------- "I have simply studied carefully whatever I've undertaken, and tried to hold a reserve that would carry me through." - Charles A. Lindbergh. "As for background noise level; 35 dBA is a good classroom; 45 dBA is a sound masking system!" - Anthony K. Hoover > After a second look, I am not clear on the third worksheet (Resonant > Modes). I would expect that the top graph would be a room response for [quoted text clipped - 4 lines] > > Angelo Campanella After some more turning things over in my mind, I can better describe what I was aiming at here. The column graph on sheet "Resonant Frequencies" shows the frequency of each mode after they have been sorted into ascending order (sorted by mode order within frequency). The smoother the curve, the better the modal distribution in the room. Conversely, the more stair-case like the plot, the more the modes are bunched together, which in turn, will produce colouration in the room. Since the column plot only shows modal frequency, and not the relative amplitude of each mode, I thought that I should attempt to display the contribution made by each mode to the overall sound field. My general assumption is that the higher the mode order, the lower its contribution to the overall field. Hence the calculation of mode attenuation. This shows the proportional reflectivity of the room surfaces at a given frequency after each mode has been reflected N times - where N is the mode order. This plot is then laid over top of the mode number/frequency plot. Since the lower order modes experience fewer reflections, I would expect them to make a more significant contribution to the overall field. I think the right hand Y axis should not be called "Attenuation", but something like "Effective Reflectivity". Anytime this ambiguously named "attenuation" plot (in yellow) shows a spike, what you are seeing (against the scale on teh right hand Y axis), is the effective rho value for the room at that frequency. Comments? Chris W |
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