As far as the dynamic range problem goes and how it correlates to the listener I think you should make a list of possible alternatives for causation of compression. Including the fact that most everything audio based will be run through compression by the mastering engineer. But also I think what can get overlooked is a cocktail party like effect.
To me the cocktail party effect sounds like a side chain compressor or a "ducker". A simple example of this is on the radio if there is an ad or the DJ is talking with music in the background as the person talks the background sounds get compressed. It doesn't seem to be as blatant as an electronic compressor but still I don't think you can overlook the possibility that if you turn something up too loud that their brain could start to perceptually compress the signal when there is absolutely nothing going on with the speakers or electronic signal.
To me the cocktail party effect sounds like a side chain compressor or a "ducker". A simple example of this is on the radio if there is an ad or the DJ is talking with music in the background as the person talks the background sounds get compressed. It doesn't seem to be as blatant as an electronic compressor but still I don't think you can overlook the possibility that if you turn something up too loud that their brain could start to perceptually compress the signal when there is absolutely nothing going on with the speakers or electronic signal.
or amplitude
I don't understand the top paragraph, but as to line sources, they don't interest me either, but these concepts are common to ALL forms of sound radiation where directivity is involved. Its not specific to line sources.
Ok. VC heating, transient analysis:
What the first 3 figures will show is a tweeter subjected to a steady state sine wave at a specific RMS power level. The temperature is allowed to come the quasi-steady value determined as the temperature it would reach if the power were delivered at DC. Then I look at the effect of frequency on the oscillation of T about the quasi-steady value and the HD in the current flowing through the VC. The frequencies are chosen to show the ability of the temperature to follow the input power and are not intended as realistic frequencies to driver the tweeter.
10 Hz. The temperature is able to follow the power to some degree but the thermal response lags the power. As a result, the VC resistance and driver sensitivity also follow temperature. While there is no change in amplitude form cycle to cycle the plot to the right shows that there is HD generated due to the temperature fluctuations. Only odd order harmonics are present indicating that the temperature variation is symmetric about the mean level. 3rd odder HD runs about 1%.
100 Hz. With the frequency increased to 100 Hz the temperature variation shows that it is just about constant. The frequency is sufficiently high that the VC temperature can not follow the power variation and the temperature remains very nearly at the quasi-steady value. Sensitivity and VC R thus remain constant as well. Thus, which the VC heating result in compression form the cold Re value, there is no significant dynamic effect on SPL. However, even though the compression is not significant, there are distortion components generated, as shown to the right. In this case the 3rd order HD is about 0.1%, a factor of 10 reduction with the factor of 10 increase in frequency.
1 k Hz
At 1 K Hz there are no variation in and parameters visible on the scale of the figure. However, the distortion plots show that there is still some small variation with 3rd order HD at a level of 0.01%, another 10 fold reduction with at 10 fold increase in frequency. Obviously, increasing the frequency to 10 K Hz would result in another order of magnitude reduction in HD.
The last figure is a little more complex. In this case the input signal is a 1 k Hz amplitude modulated at 125 Hz. The figure shows that there is some small dynamic effect on temperature but nothing that would likely be audible in terms of SPL. However, the distortion plot tells a different story. In this figure the red diamonds with black out line represent the harmonic content of the output current. Notice the two dots at 875 and 1125 Hz have black centers. The black dots represent the harmonic content of the input signal (sum and difference. 1000 +/- 125). Thus the remaining dots w/o black centers represent distortion arising from thermal effects. Note also in this figure that the temperature level is overall lower that that for a pure sine wave. This is as expected as the mean power is also lower although the peak power remains the same.
These simulations lead me to conclude that dynamic compression in a typical hifi tweeter, in the sense that a sharp transient will be reproduced at a reduced SPL due to VC heating to the transient signal, is not significant. Rather the VC temperature will follow a meandering values associated more closely with the time variation of the mean power level over a much longer time scale. However, distortion associated with the transients may have a components which are highly dependent on the actual form of the signal.
For those interested in the numerical accuracy of the simulations it is noted that all simulation were performed with the same relative accuracy. That any numerical error is sufficiently small is indicated by the consistent reduction in 3rd order HD as the frequency increases.
Keep in mind that these are simulations and while I have attempted to model the thermal effects reasonably, without specific data it is difficult to judge if the assumptions made regarding cooling are of sufficient accurate. The rate of heat generation is fairly easy to calculate given the VC length, diameter, number of layers and cold resistance. Cooling rates must be estimated. However, it must be recognized that for the temperature to follow the transient more accurately would require faster cooling. But fast cooling in contrary since faster cooling would mean the VC would not heat up as much under any conditions.
What the first 3 figures will show is a tweeter subjected to a steady state sine wave at a specific RMS power level. The temperature is allowed to come the quasi-steady value determined as the temperature it would reach if the power were delivered at DC. Then I look at the effect of frequency on the oscillation of T about the quasi-steady value and the HD in the current flowing through the VC. The frequencies are chosen to show the ability of the temperature to follow the input power and are not intended as realistic frequencies to driver the tweeter.
10 Hz. The temperature is able to follow the power to some degree but the thermal response lags the power. As a result, the VC resistance and driver sensitivity also follow temperature. While there is no change in amplitude form cycle to cycle the plot to the right shows that there is HD generated due to the temperature fluctuations. Only odd order harmonics are present indicating that the temperature variation is symmetric about the mean level. 3rd odder HD runs about 1%.
An externally hosted image should be here but it was not working when we last tested it.
100 Hz. With the frequency increased to 100 Hz the temperature variation shows that it is just about constant. The frequency is sufficiently high that the VC temperature can not follow the power variation and the temperature remains very nearly at the quasi-steady value. Sensitivity and VC R thus remain constant as well. Thus, which the VC heating result in compression form the cold Re value, there is no significant dynamic effect on SPL. However, even though the compression is not significant, there are distortion components generated, as shown to the right. In this case the 3rd order HD is about 0.1%, a factor of 10 reduction with the factor of 10 increase in frequency.
An externally hosted image should be here but it was not working when we last tested it.
1 k Hz
At 1 K Hz there are no variation in and parameters visible on the scale of the figure. However, the distortion plots show that there is still some small variation with 3rd order HD at a level of 0.01%, another 10 fold reduction with at 10 fold increase in frequency. Obviously, increasing the frequency to 10 K Hz would result in another order of magnitude reduction in HD.
An externally hosted image should be here but it was not working when we last tested it.
The last figure is a little more complex. In this case the input signal is a 1 k Hz amplitude modulated at 125 Hz. The figure shows that there is some small dynamic effect on temperature but nothing that would likely be audible in terms of SPL. However, the distortion plot tells a different story. In this figure the red diamonds with black out line represent the harmonic content of the output current. Notice the two dots at 875 and 1125 Hz have black centers. The black dots represent the harmonic content of the input signal (sum and difference. 1000 +/- 125). Thus the remaining dots w/o black centers represent distortion arising from thermal effects. Note also in this figure that the temperature level is overall lower that that for a pure sine wave. This is as expected as the mean power is also lower although the peak power remains the same.
An externally hosted image should be here but it was not working when we last tested it.
These simulations lead me to conclude that dynamic compression in a typical hifi tweeter, in the sense that a sharp transient will be reproduced at a reduced SPL due to VC heating to the transient signal, is not significant. Rather the VC temperature will follow a meandering values associated more closely with the time variation of the mean power level over a much longer time scale. However, distortion associated with the transients may have a components which are highly dependent on the actual form of the signal.
For those interested in the numerical accuracy of the simulations it is noted that all simulation were performed with the same relative accuracy. That any numerical error is sufficiently small is indicated by the consistent reduction in 3rd order HD as the frequency increases.
Keep in mind that these are simulations and while I have attempted to model the thermal effects reasonably, without specific data it is difficult to judge if the assumptions made regarding cooling are of sufficient accurate. The rate of heat generation is fairly easy to calculate given the VC length, diameter, number of layers and cold resistance. Cooling rates must be estimated. However, it must be recognized that for the temperature to follow the transient more accurately would require faster cooling. But fast cooling in contrary since faster cooling would mean the VC would not heat up as much under any conditions.
But as I keep saying, this is not the issue in my mind. Music is not a single sharp transient. So your conclusion may be valid for this obscure signal, but its not for music.
Thank you for your contribution to this topic. I started reading your book and it is clear if anyone here can grasp this math it is you. I'm having a hard struggle with it.
Perhaps it would be nice if we could end with some pragmatic considerations?
Earl, do you think dispersion actually happens in audio reproduction, be it domes, horns or panels? And, to your best judgement, does it need more looking into (is it a problem?).
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Dispersion would happen, but it would be extremely small and not a effect worth worrying about. The only place where it was even notable was for small distances at high mode numbers, any real transducers could not really excite such a situation. So while these effects exist on paper they are not consequential at all.
The understanding of directivity and what the theory of modal radiation tells us about it is however critical to understand if one is concerned with directivity, as I am. If there is a single subject that is under utilized in loudspeaker design it is directivity. Its hardly ever considered in the designs, and the resulting systems polar performance in this regard shows this - but of course the manufacturers don't want to show this to you, so they will play down their flaws and play up their strengths. Even if these are completely irrelavent.
I would add that dispersive errors are far greater in a typical crossover than form any frequency dependents of the phase velocity for a wave propagating in air.
Some more info on thermal heating.
The first figure shows the thermal time constant for a tweeter as a function of the maximum allowable VC temperature. As previously stated, the properties of audio ferrofluids would seem to dictate that the max VC temperature would be in the 200 to 400 C range with a time constant between 0.146 and 0.42 sec. These would correspond to between 2 and 7 Hz. Note that to cool by 5% takes a time of 0.05 time constants which at 200 degrees would be 7.3msec or 135 Hz. A 5% change in temperature for 200 degrees C would be only 10 degrees and a change in VC resistance of 3.9% or Re. Higher allowable VC temperature requires longer time constants.
The next figure shows the maximum rate of temperature increase for an incremental change in power. For example, if the system were suddenly subjected to an increase in applied power of 100 watts, then the maximum rate of temperature increase would be about 1.5 C / msec. This maximum rate would only exist at the instant the power level changed and after that the rate of increase would decrease with the same time constant as the cooling. In other words, if the cooling time constant is 0.15 sec, then the heating rate would drop decrease by 36% after 0.15 sec of sustained power application.
The first figure shows the thermal time constant for a tweeter as a function of the maximum allowable VC temperature. As previously stated, the properties of audio ferrofluids would seem to dictate that the max VC temperature would be in the 200 to 400 C range with a time constant between 0.146 and 0.42 sec. These would correspond to between 2 and 7 Hz. Note that to cool by 5% takes a time of 0.05 time constants which at 200 degrees would be 7.3msec or 135 Hz. A 5% change in temperature for 200 degrees C would be only 10 degrees and a change in VC resistance of 3.9% or Re. Higher allowable VC temperature requires longer time constants.
An externally hosted image should be here but it was not working when we last tested it.
The next figure shows the maximum rate of temperature increase for an incremental change in power. For example, if the system were suddenly subjected to an increase in applied power of 100 watts, then the maximum rate of temperature increase would be about 1.5 C / msec. This maximum rate would only exist at the instant the power level changed and after that the rate of increase would decrease with the same time constant as the cooling. In other words, if the cooling time constant is 0.15 sec, then the heating rate would drop decrease by 36% after 0.15 sec of sustained power application.
An externally hosted image should be here but it was not working when we last tested it.
VC Heating, final installment:
The following figures show the variation of VC temperature using sampled music as the input voltage. Since we are talking about a tweeter, the signal was passed through an LR4 1k Hz high pass filter before sampling. Thus the signals are what would reach the tweeter. Level has been set arbitrarily and do not necessarily represent true playback levels.
Soft Rock (Steve Winwood, Higher Love)
Jazz (Earl Klugh, Across the Sand)
Chopin, Polonaise:
Symphonic, (Stravinsky, The Rite of Spring)
All the results show that the VC temp does not follow the transient, but rather response slowly to changed in the mean power level. There is no short term dynamic compression due to thermal effects.
If I find any better data whcih would alter these results I'll post corrected simulations. But for now this is as far it goes.
The following figures show the variation of VC temperature using sampled music as the input voltage. Since we are talking about a tweeter, the signal was passed through an LR4 1k Hz high pass filter before sampling. Thus the signals are what would reach the tweeter. Level has been set arbitrarily and do not necessarily represent true playback levels.
Soft Rock (Steve Winwood, Higher Love)
An externally hosted image should be here but it was not working when we last tested it.
Jazz (Earl Klugh, Across the Sand)
An externally hosted image should be here but it was not working when we last tested it.
Chopin, Polonaise:
An externally hosted image should be here but it was not working when we last tested it.
Symphonic, (Stravinsky, The Rite of Spring)
An externally hosted image should be here but it was not working when we last tested it.
All the results show that the VC temp does not follow the transient, but rather response slowly to changed in the mean power level. There is no short term dynamic compression due to thermal effects.
If I find any better data whcih would alter these results I'll post corrected simulations. But for now this is as far it goes.
thanks a lot for the answers gentlemen, and good point about the crossover indeed.
Earl, like I said I'm having trouble getting through the math. When I look back at my study I remember doing calculations is Hilbert and Banach spaces, Euler sequences, applying Hilbert transforms etc but after twenty years it's just that: memories. I could really use a good book to freshen up my math skills, preferably directed towards acoustics/audio engineering. Any suggestions?
By the way I did buy the psycho acoustic books and am currently reading Toole's life work. It's not as in-depth as some of his papers but very broad and a nice read so far.
Earl, like I said I'm having trouble getting through the math. When I look back at my study I remember doing calculations is Hilbert and Banach spaces, Euler sequences, applying Hilbert transforms etc but after twenty years it's just that: memories. I could really use a good book to freshen up my math skills, preferably directed towards acoustics/audio engineering. Any suggestions?
By the way I did buy the psycho acoustic books and am currently reading Toole's life work. It's not as in-depth as some of his papers but very broad and a nice read so far.
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Many people think that when they get old its too late to learn math, or refresh what you used to know. That's not true at all. About a year or two ago I learned that physicists now believe that they have finally found the long awaited Unified Field Theory - WOW!
It dawned on me that I would be a fool to be a Physicist, to have lived at this point in time, and to not have understood this new theory. So I started reading, and reading, and reading and I'm still not there, and unlike when I was young, it doesn't all stick, but when I look back on where I started, I've come a long ways. So it CAN be done.My favorite refresher book is "Advanced Engineering Mathematics" by Kresig, Wylie's is also good. These books are plentiful and on Amazon Used should be almost free. They provide all the basics upon which my book adds the specific techniques required for transducers.
If you're into the Theory of Everything then this might interest you as well. This recent publication has the possibility to turn out into something spectacular. If it holds up it might even win a Nobel prize. The paper
Many people think that when they get old its too late to learn math, or refresh what you used to know. That's not true at all. About a year or two ago I learned that physicists now believe that they have finally found the long awaited Unified Field Theory - WOW!
I agree with you there bro. Older people don't have the same capacity for learning as young people but the real problem is they utilize LESS of their diminished capacity than young people do of their full.
It's just this societal mantra that you study for the first 20-25 years then you work for the next 40 years and then you watch TV like a retard somewhere in Florida till you die. but it doesn't have to be that way.
It's just that most people genuinely HATE learning. And i can't blame them - i don't understand how somebody could study Law for example - i would rather shoot myself. But if you loved learning in college - there is no reason why you should stop - ever.
In fact ! If you come to realize that love of learning what made you different from most other people in the first place - that it is your identity - then it is also your destiny - you simply have no choice but to keep doing it 🙂
One of the reasons I retired at 50. Love to learn how and why. Could generally care less about applications.
Very interesting, but sounds more like an alternate explaination that a revolution. But time will tell. Many times "new" theories are just alternate ways of looking at an old problem. No new physics results just different perspectives. Don't get me wrong, this is always a good thing. The new perspectives sometimes highlight previously unseen aspects.
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