How exactly is this math done?
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Introducing Directiva - An ASR open source platform speaker project
- Thread starter Rick Sykora
- Start date
How exactly is this math done?
TimW
Major Contributor
Would the orientation/location of the PRs on the enclosure affect their output?
I don't think this is possible with the current enclosure shape, but I imagine placing the passive radiators on the back of the enclosure with bracing and damping material placed in-between them and the woofer might reduce their output above tuning frequency. It might also reduce their output at tuning frequency but I don't know, this is just an uneducated hypothesis.
I don't think this is possible with the current enclosure shape, but I imagine placing the passive radiators on the back of the enclosure with bracing and damping material placed in-between them and the woofer might reduce their output above tuning frequency. It might also reduce their output at tuning frequency but I don't know, this is just an uneducated hypothesis.
I had assumed that the sound sources are incoherent. Then 90dB and 75dB would apply:
SUM = 10*log(10^9 + 10^7.5)
This is not correct as the sound sources are coherent, i.e. the phase relationship plays a role at each frequency.
For the near-field measurements of woofer and PR, after the sound level correction, the minimum phase was determined and a possible delay for the offset of the drivers was considered (diagrams without baffle-step correction)
100mm offset
150mm offset
In this way, the influence of PR in the midrange can be up to 1dB - it depends on the woofer/PR offset.
@Rick Sykora how big is the offset of woofer and PR? From the baffle to the center of the PR.
Must disagree with myself.
It's even a little more complicated than that. Since the sound radiation is no longer omnidirectional in the midrange, the influence of the PR should be less in the on-axis measurement as the on-axis sound pressure of the PR should be lower than with the +-90° measurement.
OP
- Thread Starter
- #365
I had assumed that the sound sources are incoherent. Then 90dB and 75dB would apply:
SUM = 10*log(10^9 + 10^7.5)
This is not correct as the sound sources are coherent, i.e. the phase relationship plays a role at each frequency.
For the near-field measurements of woofer and PR, after the sound level correction, the minimum phase was determined and a possible delay for the offset of the drivers was considered (diagrams without baffle-step correction)
100mm offsetView attachment 119960 150mm offsetView attachment 119961
In this way, the influence of PR in the midrange can be up to 1dB - it depends on the woofer/PR offset.
@Rick Sykora how big is the offset of woofer and PR? From the baffle to the center of the PR.
from PR center to front edge is 170 mm.
I had assumed that the sound sources are incoherent. Then 90dB and 75dB would apply:
SUM = 10*log(10^9 + 10^7.5)
This is not correct as the sound sources are coherent, i.e. the phase relationship plays a role at each frequency.
For the near-field measurements of woofer and PR, after the sound level correction, the minimum phase was determined and a possible delay for the offset of the drivers was considered (diagrams without baffle-step correction)
100mm offsetView attachment 119960 150mm offsetView attachment 119961
In this way, the influence of PR in the midrange can be up to 1dB - it depends on the woofer/PR offset.
@Rick Sykora how big is the offset of woofer and PR? From the baffle to the center of the PR.
Thank you for that. I'm only barely comfortable trying to figure out what it should be for the case where the two sources are coherent. If they are incoherent, I supposed it could be almost anything, depending on whether the sources are nearly in phase or completely out of phase.
But as for the case where they are coherent, I think that if a second acoustic source is added to an existing one, and they are coherent, SPL should increase by 6 dB if they are identical and if the individual pressure values are identical, because in this situation pressure should double. Evidence for this is what happens with an LR2 or LR4 crossover where the two drivers are each at -6 dB at the crossover point. With each driver being at -6 dB, this means that pressure for each is 1/2 the nominal value, and since the pressure response with these crossovers is flat through the crossover point, it follows that pressure is twice what it would be with either driver acting alone. Which implies that absolute pressure values (not decibel values) are directly additive when coherency applies.
If I play with your formula (which you emphasize is not correct for the case where the sources are coherent) for the case where the two dB values are identical, I think that it simplifies:
SUM = 10*log(10^(X/10) + 10^(X/10)) = X + 3.
I have to confess that I didn't actually do the logarithmic algebra but only stuck in some numbers and saw that the result is X + 3. The reasoning I did above tells me that in the case where the two sources are coherent the answer should be X + 6. This leads me to infer that in the case where the two sources are coherent, that the multiplier at the front of the SUM expression should be 20 instead of 10. But I expect that you were probably keenly aware of this and are puzzled by why I'm doing this.
OP
- Thread Starter
- #367
Not much to report tonight as have been working on amplifiers and went to print a spec sheet and my HP Laserjet MFP balked. It is older and kept making me power cycle while displaying "Scanner Error 52". After researching that on the net, found it is at least a $75 part and so not going to fix.
Spent part of my afternoon getting another HP MFP to install wifi drivers. Was going to try adding some weight to the Purifi PRs, bit they are already pretty heavy and low Fs. Weather was really nice for March, so got in some yardwork. Back to Directiva tomorrow!
Spent part of my afternoon getting another HP MFP to install wifi drivers. Was going to try adding some weight to the Purifi PRs, bit they are already pretty heavy and low Fs. Weather was really nice for March, so got in some yardwork. Back to Directiva tomorrow!
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I'm impressed by the speed of this project and the technical knowledge of the participants. Very interesting read. Thank you so much!
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Thought about this some more. For two drivers coherent, the formula should be:
20 x LOG(10^(X/20) + 10^(Y/20)), where X and Y are the two individual SPL values (both positive).
For example, if two drivers are both 85 dB nominally and both are 79 dB at the crossover point (each is -6 dB relative to its nominal value), the formula gives 20 x LOG(10^(79/20) + 10^(79/20)) = 85 dB
Of greater particular interest is the question of how the stronger of two coherent sources is enhanced by the contribution of the weaker one. Without loss of generality, it is valid to set the weaker source to 0 dB, setting the stronger source X to the difference (in positive decibels).
SUM = 20 x LOG(10^(X/20) +1)
To find just the gain, for the stronger source as a result of the contribution of the weaker source, we subtract X from the previous expression:
gain applied to stronger source = SUM - X = 20 x LOG(10^(X/20) +1) - X
For example, for the case where the weaker source is -25 dB relative to the stronger source X, the formula reduces to:
gain applied to stronger source = 20 x LOG(10^(25/20) +1) - 25 = .5 dB
The following observations are potentially of value:
If the weaker of two coherent acoustic sources is -5 dB relative to the stronger one, the net SPL will be +4 dB relative to the stronger one.
If the weaker of two coherent acoustic sources is -10 dB relative to the stronger one, the net SPL will be +2 dB relative to the stronger one.
If the weaker of two coherent acoustic sources is -20 dB relative to the stronger one, the net SPL will be +1 dB relative to the stronger one.
If the weaker of two coherent acoustic sources is -30 dB relative to the stronger one, the net SPL will be +.3 dB relative to the stronger one.
If the weaker of two coherent acoustic sources is -40 dB relative to the stronger one, the net SPL will be +.1 dB relative to the stronger one.
As some others said, in the end, you trade resonances for obviously higher leakage (in a 2-way, of course, but a 3-way with a sealed midrange chamber also makes ports happy). Wonder if it's easier to fight one than the other.
It certainly does occur to me that with ports and passive radiators, the output from the port or passive radiator is much closer to the ideal in the case of a 3-way speaker where the coupled active driver cuts off at a few hundred Hz, vs. a 2-way speaker where the coupled active driver operates upwards of 2 kHz. Another reason to prefer a 3-way speaker over a 2-way speaker.
OP
- Thread Starter
- #372
Yes, has occurred to me too, but then why spend big bucks on the Purifi woofer if not taking advantages of its major audible benefits.
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OP
- Thread Starter
- #373
For a more traditional PR tuning, Rick Craig got better results with the SB passive radiator...
I have some, so am contemplating switching to it. Used it in the SPK5 cabinet with comparable results. Mulling it over with the team.
I have some, so am contemplating switching to it. Used it in the SPK5 cabinet with comparable results. Mulling it over with the team.
For a more traditional PR tuning, Rick Craig got better results with the SB passive radiator...
View attachment 120187
I have some, so am contemplating switching to it. Used it in the SPK5 cabinet with comparable results. Mulling it over with the team.
This looks decidedly better.
nit-picking:
Unfortunately, the phase relationship between the two coherent sources was not taken into account.
With your formula you calculate the maximum achievable sound addition. The possible sound level range in your example would be
So it may be that the 0.5dB will never be reached.
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OP
- Thread Starter
- #376
Ok, until I can figure out what to do with the less optimal tuning for the dual passive radiator Directiva, we have decided to shift back to the base cabinet and use the SB passive radiator with it. I am retrofitting the cabinet with the port this morning, but will be taking a break around lunch to get my first Covid shot!
If no bad reactions, should have some pics and possibly graphs later today.
If no bad reactions, should have some pics and possibly graphs later today.
nit-picking:
Unfortunately, the phase relationship between the two coherent sources was not taken into account.
With your formula you calculate the maximum achievable sound addition. The possible sound level range in your example would be 0 - 0.5 dB.
So it may be that the 0.5dB will never be reached.
If two waves are offset in phase and if this is entirely due to a difference in the distances between the detection point and the two origination points, they are not considered coherent waves even if it happens that they would be perfectly in phase were it not for the spatial offset.
It may well be true that at wavelength equal to twice the difference in the two distances (the distance from the detection point to the two respective origination points), the weaker signal will be 180 degrees out of phase with respect to the stronger signal. I expect this will be true if the movement of the passive radiator is in phase with the movement of the cone (at frequencies where they are both moving). So what happens in this scenario where the phase relationship is 180 degrees? Instead of .5 dB (or whatever) being added, it will be subtracted. The additive effect, in spite of being negative addition, is as strong as it is for the case where the phase relationship is 0 degrees. Clearly, what we are talking about is a comb filtering effect, for frequencies above a threshold somewhere in the lower midrange.
For detection points along the horizontal plane but well over to one side, say 75 degrees off the center axis, the side-mounted passive radiator may be the stronger source of sound pressure at frequencies where both the active and passive radiators are moderately directional. In spite of the ad hoc nature of any attempt to come up with a rule of thumb, a rule of thumb of some sort is needed, toward avoidance of the comb filtering effect. If I take a stab at this, it seems to me that at wavelengths not adequately longer than the distance separating the two drivers, the peaks in the response of the passive radiator should be -20 dB relative to the response of the active driver. Perhaps the fuzzy transition in wavelength should be where the distance separating the the active and passive driver is 1/3 of the wavelength. In other words, perhaps the -20 dB rule should apply, in a fuzzy way of course, to frequencies where the wavelength is not at least 3x greater than the distance separating the active and passive drivers. If this fuzzy rule is applied to the Directiva, the fuzzy transition point is probably somewhere in the fuzzy ballpark of 400 Hz.
Ok, until I can figure out what to do with the less optimal tuning for the dual passive radiator Directiva, we have decided to shift back to the base cabinet and use the SB passive radiator with it. I am retrofitting the cabinet with the port this morning, but will be taking a break around lunch to get my first Covid shot!
If no bad reactions, should have some pics and possibly graphs later today.
I've had both shots of the Pfizer, the 2nd one two weeks ago. I had some slight soreness with both, not much different from an annual flu shot. I had some slight bruising/yellowing with the first one, but not with the second one. No other reactions that I could identify definitively with either shot. The strongest effect by far was the peace of mind.
OP
- Thread Starter
- #379
Got some Pfizer vaccine and am feeling fine. Here is reworked back baffle. Forgot a before pic but not hard to imagine as there was only a port and a speakon cutout. The port has been covered and will likely get a speakon and the speakon was cutaway with the SB passive radiator cutout. Note some of the back part of the brace has been removed too...
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Steve Dallas
Major Contributor
I got the 1st dose of Moderna last week. No side effects other than a sore arm for 2 days.
I'll take that over COVID, which I had last October. I am an long hauler and am not loving life right now. One of the worst parts is that it affected my hearing. Loud tinnitus and a new sensitivity to sibilants. Hopefully those go away over time.
I'll take that over COVID, which I had last October. I am an long hauler and am not loving life right now. One of the worst parts is that it affected my hearing. Loud tinnitus and a new sensitivity to sibilants. Hopefully those go away over time.
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