Acoustic gain, G (Strength), total, early and late
A spreadsheet for calculating G and portions of G before and after 80 ms (Ge and Gl) at different source-receiver distances (r) (56 kB). The theoretical direct sound level (Gd) is also included. The calculations are based on measured G and C80, or based on measured T and V, the latter using Barron’s Revised Theory.

Old spreadsheets can be found here:
Calculating Gl (and Ge) (11 kB) based on measured Strength (G) and clarity (C80).
Estimating Gl (18 kB) based on measured reverberation time (T), hall volume (V) and source-receiver distance (r).

Direct sound and floor reflection interference comb filtering vs frequency and distance
A spreadsheet for calculating comb filter interference versus frequency
(214 kB). A comb filter related to the direct sound will not only change the frequency response of the sound. It will, maybe more importantly, also contribute to drastically reduce the ratio of direct sound and reflected sound for sound within enclosed spaces and consequently reduced clarity and speech intelligibility. So keeping track of possible comb filters can be worthwhile!

A spreadsheet for calculating comb filter interference versus distance (383 kB). A comb filter interference can be observed in terms of the total level at a single frequency at difference distances from the source, instead of at different frequencies at one single position (source-receiver distance). This spreadsheet can be used to estimate the combined level of the direct sound and floor reflection within the orchestra at lower (single) frequencies, as described in my PhD thesis Chapter 4 and the October 2010 JASA paper (see above).

Total sound level
A simple spreadsheet for calculating total sound levels (277 kB). The total level can be found for coherent, phase shifted coherent and uncorrelated sources. Additionally, the level change for two coherent source can be found as function of phase relation.

Disclaimer: The spreadsheets are available for use at own risk.

1. Daniel

Do you have any bibliographic references that support the equations on these spreadsheets?

• Dear Daniel,

The spreadsheets on G with estimations of early and late reflected sound levels are based on Barron’s Revised Theory, available in Barron’s book “Auditorium Acoustics and Architectural Design”.

The calculations of Ge and Gl from G and C80, comb filtering and total levels are based on basic wave phenomena and level calculations (logarithm ratios). See for instance http://en.wikipedia.org/wiki/Comb_filter, http://en.wikipedia.org/wiki/Sound_pressure and Barron’s book. Harry F. Olson’s book “Acoustical Engineering” may also be a good reference.

I hope this was of some help. Feel free to ask if you have any further questions or comments.

JJ

2. Daniel

Hello Jens, thank you for your kind and fast response.
At this moment I’m studying the comb filter phenomena caused by two sources whose distance d1 and d2 from a measuring point could not be the same; and I was wondering on how to obtain a mathematical model for this. At first I thought I could use the wave interference theory, then I looked into several links as the Wikipedia article and I understood that, if we model the situation using a feed forward system, we obtain a transfer function whose magnitude is |H| = √[(1+ α²) + 2α Cos(ωK)]. I searched into Barron’s, Olson’s and physics books for a more physical approach that could explain the meaning of the factors α and K, but didn’t find anything related. So I dig into the spreadsheets and concluded the following:

1) α = γη where γ is the relative polarity of the second source (±1) and η is a relative linear level obtained from η(dB) which is obtained from the log. relationship of the distances (which I understood after reading the Wikipedia article on sound pressure) minus the excess reflection attenuation – As I’ve never heard of this last term, I searched and found this: http://noisemapping.com.au/Software/PenHelp/index.html?ground_reflection.htm – Is this ‘ground reflection attenuation’ (in dB) the same you subtract when calculating the η(dB)?

2) K is the sum of the difference (d2-d1) divided by the speed of sound (which is a function of the temperature in °C) plus an excess reflection delay in ms. I didn’t find anything concerning this last term.
I’d like to know if everything I concluded in 1) and 2) is correct.

So my main question, which can be divided in several questions, is, If we start from a block model to find the transfer function |H|, ho do we relate the factors α and K to the physical system consisting of two sound sources? What is the physical meaning of α and why is it defined as α = γη?
The same goes for the K factor.
There’s a lot of new terms for me in these equations, such as the excess reflection attenuation, the excess reflection delay, is there a book where I could find more information about this?
Excuse me if I extended this too much, but I’ll be really grateful if you can explain this to me, as long as I’ve not been able to find further information about comb filters in such an specific way.
Greetings!

• Hello Daniel,

Here is my attempts at explaining the physical meaning of K and α:

K is the time delay (measured in seconds) representing the difference in time of the arrival for the two interfering waves at the receiver point. In my spreadsheet K is based on the difference in propagation distance, d1 and d2, K=c/(d1-d2) where c is the speed of sound. But any additional delay can also be given that will be included in K. Signal delay between loudspeakers may be one example of additional delay. By multiplying K with ω we get the corresponding phase-shift measured in radians. With no level difference between the waves at the receiver point the summer pressure amplitude can be expressed as √[2(1+cos(ωK))], where the each wave has an amplitude of 1. The deviation of sound power level relative to only one of the waves present will be equal to the square of |H|.

With different propogation distance, d1 and d2, the inverse-square-law will introduce a level difference between the waves. We can also have excessive attenuation for instance with a sound aborbing floor in the case of one source and a floor reflection. In my spreadsheet the inverse-square-law contribution is autmatically included based on d1 and d2, and any excess additional attenuation, for whatever reason, can be given. With totally 6 dB level difference we will have a scaling factor α equal to 0.5, in other words α = 10^(-ΔL/20), ΔL being a positive value.

I have also given the option to switch polarity between the sources, resulting in the cosine term being multiplied by -1.

If only considering the case where the waves are fully in phase (phase-shift = integer multiples of 2π), |H| will be equal to 1 + α [since 1 + α^2 + 2α = (1+α)^2]. Similarly if the fully out of phase case |H| will be equal to 1 – α. The maximum and minimum level of the comb filter, seen relative to the level of the loudest source isolated/alone, can therefore easily be calculated as 20*log(1 – 10^(-ΔL/20)) and 20*log(1 + 10^(-ΔL/20)).

I hope this was of some help for you. Feel free to ask if you have any further questions.

What kind of practical wave interference situation are you investigating? Are you working within the field of acoustics too?

Greetings!

3. Daniel

Hello Jensen.
Excuse me for my delay, this was a hard week. Your information was very clarifying! I think can finish my first project with this ideas along with some comprehensive texts I found on the web. I’ve worked in the live sound field calibrating sound systems using Meyer Sound’s SIM3; now that I’m studying electronic engineering I wanted to have a more mathematical and physical approach to the comb filter phenomena, as it was for me nothing more than a concept. I’m looking forward to write an interactive program in C++ to calculate and display a comb filter under several conditions. Something very similar to the spreadsheets you share here, but adding some extra and basic tools such as sound speed calculation, wavelength/frequency calculations, etc. which are very useful when working on the field. Of course it’s going to be free, I’ll post it in my blog – http://deltaphiblog.blogspot.com/ – (it’s in spanish, if you don’t speak it you could use google’s translate tool on the right) once it’s ready (although I think I’ll have to wait until I’m on vacation). I’d like to put your name in the acknowledgements part of the program, if you don’t mind.

Thank you very much!

• Hello Daniel,

Good to hear you got something out of my attempt on clarifying. An interactive program for basic wave calculations sounds good! I’ve had a similar free Android/iPhone app on my list too, but I have no time for it at the moment (maybe a collaboration on it some time in the future could be good?). I’ll follow your developments with interest, please feel free to update me when you’ve made some progress. Being mentioned in your acknowledgements would be an honour.

Cheers

4. Daniel

Hello Jensen, thank you for your interest and your help. Of course it will be great to collaborate in a project like that, it sounds really nice. I’ll let you know once I have something, in the mean time I’m going to learn more about creating visual applications with C++.
Cheers!