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jmebara12-Amethyst
12-Amethyst
June 28, 2018
Question

Narrow band plot(dB vs linear frequency) to 1/3 Octave band plot(dB vs 1/3 Octave band) with Prime 4

  • June 28, 2018
  • 1 reply
  • 12334 views

Hello to all expert Mathcaders 🙂

 

I have to preface my question by saying that I am a newbie in the whole field of acoustics. I am however an expert in structural analysis. So please answer my question keeping in mind that fact. I now find myself in a situation where I have to determine the structure-borne sound/sound transmission characteristics of rubber structures. With the aid of harmonic analyses, I can determine the sound transfer function (in dB) and the so called transmission loss (also in dB) of the these structures. I can then make plots of for example transmission loss (in dB) versus frequency (Hz). However, the x-axis, which is the frequency is a linear distribution of the frequencies which corresponds to the frequencies as derived from the harmonic analysis. So let us say I performed my harmonic analysis for a frequency range from 0Hz to 500 Hz at intervals of 1Hz. That means that I have 501 result points for the frequency and the determined values of the transmission loss (in dB). I now make a plot of the transmission loss vs the frequency in excel, the frequency axis (horizontal) being logarithmic and the transmission loss on the vertical axis. So far, I get good curves which correspond to my expectation, when I use the mentioned methodology.

 

However, any one who has the slightest idea in sound analysis or machine acoustics, knows that my above representation could be characterized as a so called narrow band (Please correct me if I am wrong with this denotation but that is what I have gathered, speaking to some experts). Acoustic engineers generally however want the frequencies to be represented in a 1/3 Octave Band. My limited understanding of the 1/3 Octave Band is that it has to do with some kind of summing or averaging of the frequencies depending on the outcome that is needed and the results present that need to be analyzed. I may not know exactly what the 1/3 Octave band is all about but I know that I am required to present my results of, for example transmission loss (in dB) vs frequency (Hz and log scale) on a plot that is transmission loss (in dB) vs frequency (in 1/3 Octave band scale).

 

I will love to do this in Mathcad Prime 4.0 but have no idea how and where to start or if this is at all possible in Mathcad Prime 4.0. I do however know that it is possible to get the plots I need using some kind of Matlab code and acoustic engineers are fond of using Matlab for this "Octave band analysis". I will therefore be grateful if some Mathcad Prime expert can help me achieve the desired plot in Mathcad Prime 4.0, if it is possible to be achieved at all.

 

PS: If someone is kind enough to help, the person can basically use any set of data for the transmission loss and the frequency, But if that is not possible, I could provide some trial values which could be used for the help. Assuming that all of this possible in Mathcad at all.

 

Thanks very much and looking forward to your feedback.

1 reply

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-MFra-21-Topaz II
21-Topaz II
June 29, 2018

Hi jmebara,

The following is an example of a Bode diagram of the transfer function of a system, in which the 1/3 octave bands are highlighted:

0.33octave band.jpg

 

J
jmebara12-AmethystAuthor
12-Amethyst
June 29, 2018

Hi MF.

 

Thanks very much for your quick response. First of all, the plot of the transfer function in dB vs frequency (log 10 scale), which you have posted is similar to the kind of plots that I am trying to analyze. So that's the right direction 🙂 Thanks for also highlighting the octave band regions. Gives me a visual depiction.

 

If I understand what you have shown, the Sound Levels of the transfer function in each 1/3 Octave band have to be summed up (or averaged?) to the maximum frequency based on the definition of the 1/3 Octave band filter? i.e. some kind of spectral analysis? As I said in my post, I do know some acoustic engineers who have written codes in Matlab for 1/3 octave band filters which they use for such spectral analysis (if that is what it is called). As I have seen on some Websites while doing some Research (e.g. here http://www.sengpielaudio.com/calculator-octave.htm), such summing up gives rise to some kind of "bar Chart" (if I could primitively call it as such) with the bars located at the center frequency of the 1/3 octave band. The Matlab codes I have seen however create a smooth line x-y plot and not just a bar Chart.

 

The big question is how do I transform the bode plot (e.g. the one you have posted) to such a smooth line x-y plot of transfer function sound Level vs frequency (1/3 octave band)? Is there some Kind of code that can be written to create 1/3 octave band filters which can be used to automatically generate the requeired plot? It is probably a challenging task to do this in Mathcad and I am not a good programmer to know how to achieve what I wish in Mathcad. Hoping that someone who is good at this can help me to achieve this in Mathcad.

 

Thanks

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