Finding a solution with angles and given points in a theorised sound field... of sorts.
Hello Max (and hopefully Maths) aficionados,
I am currently in the process of putting together a basic program that calculates noise attenuation of an external barrier. It takes various features and I have built modules alongside it that replicate real-world physical properties of sound, to some level, which will produce a final "auralized" value. It is simply for learning purposes and hope to build them out soon into something more significant.
But I am at the stage where I need help, and hopefully someone or a collection of people can either point me in the right direction or save me from drawing out another path of logic to solve this string of errors.
From the example there is the values provided to which I input, values go both into the 'p Trig for Zones' where I am calculating the Trig values of this particular example, and into the 'Path Length Difference' of 'A, B and C'. The issue I have is that the final equation found in 'p dB Level per Octave' concerns what is called the "Shadow Zone" , where the Source and Receiver are obscured by the height of the barrier, taking 'C' as the direct path of sight.
Ideally what I would like to happen, and I know somewhere deep down, is a way of calculating when the line of sight becomes clear, say for example in this sketch below.
Theta B should be pinned to the top of the barrier in a full circle, I feel, but I could be incorrect, but there is an important relationship (of which I am unsure of, hence my plea) between the line of sight between S and R (source and receiver) and when it crosses the boundary.
The program I hope would recognise this clear line of sight and trigger a bang in the 'p dB Level per Octave' where the expression 'expr 10*log10(3 + 20 * $f1)' to a new expression, an "illuminated zone"
I could be in too deep, I could be right on the cusp... Who knows, but if it is not clear please let me know.
Thanks,
Sam
not beeing familiar with emulation of sound barrier releated stuff, i still would claim that its physics does not look so much different than the sound from a slow or still source.
you just have to exclude (speed of sound source moving == speed of sound) because that wont happen in real world, pressure would always finds its way to the sides and not accumulate until black hole. :)
what is that "per octave" stuff about, you have sources for that?
to artificially create that in DSP you would just assume that (twice as far == SPL(linear)/ 2.) and then apply a certain type of lowpassfilter to it to roughly model air absorbtion.
Thank you for your reply Roman.
It is actually not the distance in this scenario that I am interested in here, but the recognition of the angle Theta B and when it changes its line of sight.
Below is a perhaps better example from R.J. Peter's 'Acoustics and Noise Control'.
In this example side 'C' is obstructed by the height of the barrier, so would fall into the the 'Shadow Zone', which in the 'p dB per Octave is the calculation for this. Which is used in Maekawas calculation for Noise Barriers. I need to some how work out I would tell Max to recognise an scenario where s if the source or receiver (side C) is no longer obstructed by the barrier, the 'illuminated zone' that it can trigger a bang where I can change to a new calculation. In terms of the formulae they are slightly difference between the zones.
Sam
But for my next steps the use of air absorption is important and the use of a filter should hopefully get me there, so thank you for those reminders!
to clarify; you are looking to find out whether the Receiver has LoS to the Source, and thus, if it's "illuminated" or not?
I wrote up a whole thing, but then I checked your patch, and you already have some pythagorean math stuff in there, so I don't want to wade around in that, if that's not the issue? I'm honestly having trouble reading your math, because it's all those interconnected expressions.
Hi Wetterberg,
That's right, so in the example I posted last, the diagram of Receiver and Source it is obscured by the angle of the barrier. In the small sketch I made (first post), is a scenario where the LoS is no longer obstructed, here it would fall into the illuminated zone, thus triggering a new calculation (where in p dB per Octave, a new sum would be selected to indicate this).
I was hoping that the labelling would help, but I can see where the complexity lays in understanding the way they are interconnected here. In the 'p Trig for Zones' this is calculating the diagrams angle (shadow zone) so somewhere in there, I feel, lays the answer....
Here are the equations behind the summing of the dimensions.
Hb = Height of Barrier
Hs = Height of Source
Hr = Height of Receiver
Ds = Distance from Source to Barrier
Dr = Distance from Barrier to Receiver
while i can read your patch, i still dont understand what the whole thing is about. (raytracing? both audio and an associated GUI? but ignore that, as it could be as well my lack of concentration.)
however, you seem to ignore preexisting solutions and try to do your own research instead - and i would be the last one who recommended against this method; i think it´s great. :)
Thank you Roman, it is to calculate the Noise Barriers Attenuation.
When the example values are inputted at the top, its calculations output 1/1 Band Octaves under the 'p dB Level per Octave', this is how much sound would be attenuated by the Noise Barrier (of course, minus all other variables including those you mentioned, air absorption and the distance travelled (for example, a point source attenuation from source the receiver (4(pi)(r^2)). Its aim, in the end, is to give a simulation of what it would be like at the receiver position considering these points (when all the modules are applied).
This is currently just the barrier attenuation.
Here I am interested in the recognition of the placement of source and receiver to the barrier and the line of sight and Max recognising this. It is likely in the trigonometric principles with the correct logic
It has been great seeing all the numbers output the results that match, and will be even better when the additional variables of sound attenuation are also added for a better simulation.
okay, so I was right about your intentions (I think)
here's what I wrote up before:
following the picture you linked, figure 2.14, we have enough information to draw two right-angled triangles, one on either side.
Those will help us infer (is that what it is?) the missing values.
left side:
tan^-1((Hb-Hs)/ds) gets you the angle of transmission from the source (we have both the adjacent and opposite length)
That angle continues on the right side of the barrier, where we don't have the "opposite" length, but you now have the angle, and you have dr of that side's right angle triangle - the "adjacent", so we can calculate the "opposite" in a similar fashion, and then simply add the barrier height Hb to that, Hb being the distance from the ground up to the start of our second right-angle triangle.
it's all that "sohcahtoa" trig stuff, a lot of stuff, like hypotenuse lengths can be ignored in this, since you're just trying to determine LoS, not distance from source.