David - I dug through some old textbooks, and what you present seems to be correct.
What if the sound pressure is not uniform through the solid angle? The pressure you calculate would be an average SPL across the angle. This would be the case with a non-omnidirectional radiator like a typical speaker, and a large solid angle. If the angle is pi/100 there may be no practical SPL gradient across the angle, but certainly with an angle of pi/3 or greater there would be enough gradient that the SPL calculated from acoustic power is non-representative, except as an average.... And this seems to be the exact point that @mabat was making.
Perhaps I have misunderstood your point, or maybe I got the math wrong... thoughts?
j.
I only explained what's the meaning of the power response curve and how it's calculated, which there seems to be some confusion about 
(I think it's actually very close, if not equivalent, to the sound power calculation in the CEA-2034 but I haven't checked.)
What David McBean posted is correct but also adds nothing to the discussion, as far as I can see. The reason why he posted that is unknown to me, it's like posting 2+2=4 in any place of any discussion. Perhaps he just wanted to be right
(I think it's actually very close, if not equivalent, to the sound power calculation in the CEA-2034 but I haven't checked.)
What David McBean posted is correct but also adds nothing to the discussion, as far as I can see. The reason why he posted that is unknown to me, it's like posting 2+2=4 in any place of any discussion. Perhaps he just wanted to be right
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Hi Jim,
I sincerely hope so as the method has been used in Hornresp and its predecessor programs for more than fifty years to calculate the power response chart.
(The chart shown in the attached photo was produced in 1970).
Then by definition we have a pressure response, not a power response.
The power response is useful when considering the performance of bass loudspeakers, where directivity is not an issue.
Kind regards,
David
I sincerely hope so as the method has been used in Hornresp and its predecessor programs for more than fifty years to calculate the power response chart
.(The chart shown in the attached photo was produced in 1970).
Then by definition we have a pressure response, not a power response.
The power response is useful when considering the performance of bass loudspeakers, where directivity is not an issue.
Kind regards,
David
Attachments
In Post #12,127 you posed the question "So you convert this total power back into an average pressure, but what pressure is that".
In Post #12,137 I showed how to calculate that pressure and convert it to SPL.
In Post #12,133 you stated that DI is "a difference between a selected SPL curve and the SP curve". By SP I assumed that you meant sound power.
In Post #12,138 I gave the definition of directivity index and attached a series of screenprints showing different aspects of directivity and how they are interrelated. The first attachment showed the difference between a power response and a pressure response. It is clearly not showing the directivity index.
That is why I posted.
Not unlike you, it would seem.
To all who still haven't get what we are talking about (David McBean being obviously one of them):
Measuring SPL responses on a (spherical) surface around the source is a method of estimating its total radiated power (which we need e.g. for DI calculation). The more points you measure, the more accurate result you get. If we measured in a dense regular grid across the whole surface, the total power would be directly proportional to the sum of squares of the measured pressure values. We could also take a square root of that and get an equivalent average pressure (or SPL), corresponding to that power.
Now, If we have an axisymmetric source, it's obvious that it's enough to take the polars in a single plane, 0 - 180°, say with 5°step. So now we have 37 SPL curves: 0, 5, 10, ... ,175, 180°. To calculate the total radiated power in this case, we again sum the squares of the pressures, but now we have to assign different weights to different values/angles, accordingly to the relative areas of the spherical surface that they actually represent (you probably have to make a skecth to get a grasp) - the values far off-axis will have much higher weights, just because they represent much larger areas, where we would measure that pressure if we did.
So we have the weights and make the weighted sum: radiated_power ~ SUM(w0*p0^2 + w1*p1^2 + ... + w36*p36^2).
This is the total radiated power. If we now make a square root of that (acutally a rms average of the pressures), we get an average pressure, which, if present in every direction would lead to the same total power, obviously. We can also convert that average pressure into SPL, which becomes the "SP" curve shown in the Ath reports:
SP = 20*log(sqrt(radiated_power)) = 10*log(radiated_power) [dB SPL]
This is exactly the method described in the CEA-2034 standard how to estimate power response and DI.
The meaning of the power response as an SPL curve ("SP") is simple, as naturally stems from the above - it's a frequency response of an ideal omnidirectional source radiating the same total power as the measured device. To calculate DI, take the direct difference in dB between the on-axis SPL curve and this SP curve.
Measuring SPL responses on a (spherical) surface around the source is a method of estimating its total radiated power (which we need e.g. for DI calculation). The more points you measure, the more accurate result you get. If we measured in a dense regular grid across the whole surface, the total power would be directly proportional to the sum of squares of the measured pressure values. We could also take a square root of that and get an equivalent average pressure (or SPL), corresponding to that power.
Now, If we have an axisymmetric source, it's obvious that it's enough to take the polars in a single plane, 0 - 180°, say with 5°step. So now we have 37 SPL curves: 0, 5, 10, ... ,175, 180°. To calculate the total radiated power in this case, we again sum the squares of the pressures, but now we have to assign different weights to different values/angles, accordingly to the relative areas of the spherical surface that they actually represent (you probably have to make a skecth to get a grasp) - the values far off-axis will have much higher weights, just because they represent much larger areas, where we would measure that pressure if we did.
So we have the weights and make the weighted sum: radiated_power ~ SUM(w0*p0^2 + w1*p1^2 + ... + w36*p36^2).
This is the total radiated power. If we now make a square root of that (acutally a rms average of the pressures), we get an average pressure, which, if present in every direction would lead to the same total power, obviously. We can also convert that average pressure into SPL, which becomes the "SP" curve shown in the Ath reports:
SP = 20*log(sqrt(radiated_power)) = 10*log(radiated_power) [dB SPL]
This is exactly the method described in the CEA-2034 standard how to estimate power response and DI.
The meaning of the power response as an SPL curve ("SP") is simple, as naturally stems from the above - it's a frequency response of an ideal omnidirectional source radiating the same total power as the measured device. To calculate DI, take the direct difference in dB between the on-axis SPL curve and this SP curve.
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It seems that some people have an almost pathological need to belittle others. I have never understood why.
"Belittling is the intentional act of making another feel worthless, empty, and dismissed. It is one of many forms of psychological and emotional abuse. Belittling another often creates a personal emptiness and void."
There's hardly anything more belittling than "answering" rhetoric questions put out of context and making the speaker appear to not know what they actually haven't asked at all.
So you either made it on purpose, or you actually don't know what we are talking about.
- So is there anything I wrote in the above post that you don't agree with? Because I'm saying just this all the time, and nothing else.
So you either made it on purpose, or you actually don't know what we are talking about.
- So is there anything I wrote in the above post that you don't agree with? Because I'm saying just this all the time, and nothing else.
Not sure which post you are referring to.
If it is Post #12,148 then I don't agree with your assessment that I "don't get what we are talking about". Surely you cannot be serious?
If it is Post #12,150 then I have no idea what you mean by "making the speaker appear to not know what they actually haven't asked at all".
I was simply trying to make a contribution to the discussion by explaining how to convert acoustic power to an equivalent SPL, because at the time there appeared to be some uncertainty on how to do that. I also gave the definition for directivity index because there seemed to be some confusion about that as well. Everything that followed is a consequence of your reaction to my initial two posts, which for some reason were obviously not welcomed.
I don't understand, could you please explain. I am only too happy to change Hornresp if something is not right.
BTW, here's an excerpt from the ANSI/CEA-2034-A:
"Sound power represents all of the sounds arriving at the listening position after any
number of reflections from any direction. It is the weighted rms average of all 70
measurements, with individual measurements weighted according to the portion of the
spherical surface that they represent. [...] Calculation of the sound power curve begins with
a conversion from dB to a scalar magnitude. The individual measures of sound pressure
are then weighted according to the values shown in Appendix C and an energy average
(rms) is calculated using the weighted values. The final average is converted to dB."
- This "sound power curve" is exactly my "SP" curve from the Ath reports, as explained in #12,148.
"Sound Power Directivity Index (SPDI) is normally defined as the difference between
the on-axis curve and the sound-power curve, expressed in dB."
- As I said. That "sound-power curve" is my "SP curve", if anyone was in doubt.
I only hope this settles the issue. I have no urge to continue quibbling over this.
One positive result of this debate is that Hornresp will get fixed
"Sound power represents all of the sounds arriving at the listening position after any
number of reflections from any direction. It is the weighted rms average of all 70
measurements, with individual measurements weighted according to the portion of the
spherical surface that they represent. [...] Calculation of the sound power curve begins with
a conversion from dB to a scalar magnitude. The individual measures of sound pressure
are then weighted according to the values shown in Appendix C and an energy average
(rms) is calculated using the weighted values. The final average is converted to dB."
- This "sound power curve" is exactly my "SP" curve from the Ath reports, as explained in #12,148.
"Sound Power Directivity Index (SPDI) is normally defined as the difference between
the on-axis curve and the sound-power curve, expressed in dB."
- As I said. That "sound-power curve" is my "SP curve", if anyone was in doubt.
I only hope this settles the issue. I have no urge to continue quibbling over this.
One positive result of this debate is that Hornresp will get fixed
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Tom's waveguide is a very nice one: https://www.diyaudio.com/community/...-design-the-easy-way-ath4.338806/post-7216978
(That's 450 mm diameter - can't be much smaller if it should maintain the directivity down to 800 Hz.)
(That's 450 mm diameter - can't be much smaller if it should maintain the directivity down to 800 Hz.)