I thought about how to explain the notion intuitively even to those non-mathematically inclined and here's an attempt.
It still takes some maths, but very very little -
Take it as a fact for now that the total radiated power is represented by a sum of some values. These values (p1, p2, p3) correspond to SPL in different directions from the source (at some distance which we assume is large enough):
sum = p1 + p2 + p3
The key moment is the fact that if we calculate an average of these values:
p = average(p1, p2, p3),
the sum doesn't change if we substitute all the original values with the average:
sum = p + p + p
You see that for the same total radiated power (the same sum), we can imagine a source generating the same (average) SPL in all the directions.
It still takes some maths, but very very little -
Take it as a fact for now that the total radiated power is represented by a sum of some values. These values (p1, p2, p3) correspond to SPL in different directions from the source (at some distance which we assume is large enough):
sum = p1 + p2 + p3
The key moment is the fact that if we calculate an average of these values:
p = average(p1, p2, p3),
the sum doesn't change if we substitute all the original values with the average:
sum = p + p + p
You see that for the same total radiated power (the same sum), we can imagine a source generating the same (average) SPL in all the directions.
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From: Sound Reproduction The Acoustics and Psychoacoustics of Loudspeakers and Rooms Third Edition
Floyd E. Toole
p121
Sound power is a measure of the total acoustical energy radiating through an imaginary spherical surface surrounding the loudspeaker. […]. In the spinorama the sound power is estimated by calculating an energy sum of the 70 measurements on two circular orbits, with individual measurements weighted according to the portion of the spherical surface that they represent. […] Because it is an energy sum, the final curve must be computed from sound pressures, converted from dB SPL, which are squared, weighted, summed and then converted back to dB. The result could be expressed in acoustic watts, the true measure of sound power, but here is left as a frequency- response curve having the same shape and normalized to the other curves at low frequencies. [...]
Floyd E. Toole
p121
Sound power is a measure of the total acoustical energy radiating through an imaginary spherical surface surrounding the loudspeaker. […]. In the spinorama the sound power is estimated by calculating an energy sum of the 70 measurements on two circular orbits, with individual measurements weighted according to the portion of the spherical surface that they represent. […] Because it is an energy sum, the final curve must be computed from sound pressures, converted from dB SPL, which are squared, weighted, summed and then converted back to dB. The result could be expressed in acoustic watts, the true measure of sound power, but here is left as a frequency- response curve having the same shape and normalized to the other curves at low frequencies. [...]
Yes.
This is exactly what you do in the SP_calc calculation. And the same as I do in Ath to show the "SP" curve. The result is a dB SPL curve, an equivalent omnidirectional SPL corresponding to the total radiated energy (which is the sum of the weighted squares, and to "convert it back to dB" means to make a square root (->pressure) and a logarithm (->dB) of that).
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The problem with measuring acoustic power response is similar to measuring energy or power in many other situations... It is rarely possible to directly measure energy or power. We almost always have to measure other things (distance, time, temperature, force, voltage, current, pressure, velocity), and then infer the quantity of energy or power based on the appropriate mathematical relationship.
Often times the power or energy of a device or process is expressed as an equivalent measurand which is neither energy nor power, but a unit which is directly related to energy. The energy storage capacity of a battery is expressed as amp-hours, rather than as joules. The power rating of industrial cooling machines is often expressed as "tons"... a 50 ton chiller has the same cooling capacity (energy transfer power) as melting 50 tons of ice over a 24 hour period. So here we express energy in terms of mass (how strange!).
The acoustic power response radiating through an imaginary spherical surface surrounding the loudspeaker is bulk quantity... it is averaged over the whole surface. For convenience, this averaged power is expressed in terms of the equivalent dB SPL. But if you measured the response of the DUT with a mic (i.e. measuring pressure), you can not directly measure the power response. No axis corresponds to the power response... unless the DUT happens to be perfectly omnidirectional.
Thankyou, Mabat, for attempting to explain this concept in a way that people can understand.
Often times the power or energy of a device or process is expressed as an equivalent measurand which is neither energy nor power, but a unit which is directly related to energy. The energy storage capacity of a battery is expressed as amp-hours, rather than as joules. The power rating of industrial cooling machines is often expressed as "tons"... a 50 ton chiller has the same cooling capacity (energy transfer power) as melting 50 tons of ice over a 24 hour period. So here we express energy in terms of mass (how strange!).
The acoustic power response radiating through an imaginary spherical surface surrounding the loudspeaker is bulk quantity... it is averaged over the whole surface. For convenience, this averaged power is expressed in terms of the equivalent dB SPL. But if you measured the response of the DUT with a mic (i.e. measuring pressure), you can not directly measure the power response. No axis corresponds to the power response... unless the DUT happens to be perfectly omnidirectional.
Thankyou, Mabat, for attempting to explain this concept in a way that people can understand.
I've been lurking here for a few weeks now. ATH seems like an amazing tool to develop state-of-the-art waveguides.
Last week I tried to install ATH myself. I'm no software genius and it took me quite some time to get it up and running. I managed to run demo1 and generate a graph with VACS. Then I managed to make some small changes to the script op demo1 and I got a second set of graphs out of the combined software.
But yesterday and today I keep running into an issue. I can run the Boundary Element Solver, but after that, I can't calculate the 'fields at observation stage' and I can't plot the graphs. Does anyone know what this might be?
Last week I tried to install ATH myself. I'm no software genius and it took me quite some time to get it up and running. I managed to run demo1 and generate a graph with VACS. Then I managed to make some small changes to the script op demo1 and I got a second set of graphs out of the combined software.
But yesterday and today I keep running into an issue. I can run the Boundary Element Solver, but after that, I can't calculate the 'fields at observation stage' and I can't plot the graphs. Does anyone know what this might be?
Attachments
There are no observations set that ABEC recognizes. There is an Observation.txt file that contains the observation code something has gone wrong to make that not work.
Try the ST260 ABEC Project from mabat's website
http://www.at-horns.eu/release/ST260-ABEC_project.zip
You probably want to calculate spectra, not fields
Hit F7 after the mesh was solved.Don't forget to 'Save results to txt' from the same 'Spectra' menu, if you want to evaluate your simulated waveguide via the Ath report, which is generally much more straight forward at early design stages than VACS. Press ctrl + F7 after the spectra solved.
Just to clarify - For the case of a circular piston in an infinite plane baffle, and as a result of the "fixes" you have made, are you now in effect taking the DI as shown by trace 3 below, and adding that to the full-space power response to obtain the baffled piston's half-space pressure response?
If anyone wanted to check, here's a calculation of the power response for an infinite baffle case with 19 angles: 0 - 90 / 5deg
SPL_power_response = 10*log10(1/pref^2 * (w[0]*p[0]^2 + w[1]*p[1]^2 + ... + w[18]*p[18]^2))
Weights w[0] .. w[18]:
0.000476, 0.003802, 0.007574, 0.011290, 0.014919, 0.018434, 0.021810, 0.025019, 0.028038, 0.030844
0.033414, 0.035731, 0.037775, 0.039533, 0.040989, 0.042133, 0.042957 ,0.043453 ,0.021810
This power response is a frequency response (as dB SPL) of an omnidirectional source radiating the same total power as the DUT.
So if you want to calculate a DI, subtract this power response from a selected SPL response.
SPL_power_response = 10*log10(1/pref^2 * (w[0]*p[0]^2 + w[1]*p[1]^2 + ... + w[18]*p[18]^2))
Weights w[0] .. w[18]:
0.000476, 0.003802, 0.007574, 0.011290, 0.014919, 0.018434, 0.021810, 0.025019, 0.028038, 0.030844
0.033414, 0.035731, 0.037775, 0.039533, 0.040989, 0.042133, 0.042957 ,0.043453 ,0.021810
This power response is a frequency response (as dB SPL) of an omnidirectional source radiating the same total power as the DUT.
So if you want to calculate a DI, subtract this power response from a selected SPL response.
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It seems that somewhere/how "radiating through an imaginary spherical surface surrounding the loudspeaker" has become "a pressure generated by an omnidirectional source radiating that total power."
I don't think that is a correct "transformation". An "imaginary spherical surface" is not interchangeable with "ideal omnidirectional source" because they are observations from opposite vantage points.
And it is not advisable to use a description or an imposed property of a DUT itself in a DUT property definition. Toole understand this and completely avoids/omits any description of the DUT itself as per above.
I have no doubts that the involved persons here fully understand what SP really is but I do think that a definition need to be created with outmost care and one need to weigh every single word used as well as abide a few basic laws of definition design - one is: no circular references.
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