Keeping it simple:
Neglect the forces on the driver due to Rms, Cms and back EMF
Newtons law:
F = BL x V/Re = Ma,
Neglect heat rejected to the surroundings and heat sourced other than those due to dissipation in the VC:
cp x dT/dt = dQ/dt = V^2/Re
Now:
V^2/Re = M x V x a / BL
which goes to:
dT/dt = {M x V / (cp x BL) } x a
The rate of change in temperature is proportional to the acceleration of the driver moving mass. For two driver to produce the same transient they must have the same acceleration. If we further assume that the two driver have the same moving mass, same Vc wire and same Re then we have a, M and cp are constants. Thus,
dT/dt = const x V/BL.
and since Re is the same, for the same acceleration BL x V - const. Thus, V goes like 1/BL and finally,
dT/dt = const /(BL)^2
The conclusion is that even before we consider the effect of VC heating, drivers with bigger BL and all other things constant will have slow rates of increase in VC temperature for the same transient.
Next, this simple analysis will indicate the initial rate of heating of the VC. As the VC heats, Re would increase which would actually lower the force on the drivers and reduce acceleration. Thus, the analysis sets an upper limit on how fast the VC temperature can change. Drop in the correct constants and account correctly for the volume of the VC wire in the temperature equation and we should be able to estimate the temperature rise over time, and, for example, if the increase for a sharp transient of duration,td, is significant.
Neglect the forces on the driver due to Rms, Cms and back EMF
Newtons law:
F = BL x V/Re = Ma,
Neglect heat rejected to the surroundings and heat sourced other than those due to dissipation in the VC:
cp x dT/dt = dQ/dt = V^2/Re
Now:
V^2/Re = M x V x a / BL
which goes to:
dT/dt = {M x V / (cp x BL) } x a
The rate of change in temperature is proportional to the acceleration of the driver moving mass. For two driver to produce the same transient they must have the same acceleration. If we further assume that the two driver have the same moving mass, same Vc wire and same Re then we have a, M and cp are constants. Thus,
dT/dt = const x V/BL.
and since Re is the same, for the same acceleration BL x V - const. Thus, V goes like 1/BL and finally,
dT/dt = const /(BL)^2
The conclusion is that even before we consider the effect of VC heating, drivers with bigger BL and all other things constant will have slow rates of increase in VC temperature for the same transient.
Next, this simple analysis will indicate the initial rate of heating of the VC. As the VC heats, Re would increase which would actually lower the force on the drivers and reduce acceleration. Thus, the analysis sets an upper limit on how fast the VC temperature can change. Drop in the correct constants and account correctly for the volume of the VC wire in the temperature equation and we should be able to estimate the temperature rise over time, and, for example, if the increase for a sharp transient of duration,td, is significant.
For traditional drivers (ex. dome tweeter, compression driver, etc), how long does it take to achieve a steady state? seconds? milliseconds?
It has been shown that under very specific circumstances a delay of 6us can be heard. It's a far stretch to say that this effect is audible during music reproduction. Unless you can point to a paper saying otherwise I have to assume that this is your conclusion and not something which is proven.
My second point is that floor, ceiling and side wall reflections have a delay of the same order and those are not perceived as 'time smearing', or at least not that I know of.
So unless somebody convinces me otherwise I don't believe this is an actual problem of panel transducers.
By the way, can anyone recommend a good book on psychoacoustics?
If I understand you correctly - and that's pretty rare - then I don't agree - and that's pretty common. That definition would imply steady state and thats not the issue.
Basically, its unlikely to ever come to a true steady state, but its certainly hours. As I wrote before there are a wide array of different time constants involved, some at millisecs and some at minutes and hours.
First and formost read "Binaural Hearing" by Blauert, or more simple, Tooles book. Then there is Zwicker and Fastle, (forgot the name) which is excellent and the classic bible of psychoacoustics by Harvey Fletcher (very old but very good).
You're probably mixing up microsecond (μs) and millisecond (ms).
For starters and up-to-date analysis: Toole "Sound Reproduction"
Lots of older studies and details: Blauert "Spatial Hearing"
The (very) short version of Toole's book: http://www.harman.com/EN-US/OurComp...p/Documents/Scientific Publications/13686.pdf
Very recent results at Audio Musings by Sean Olive
Best, Markus
It does not imply steady state, but rather a varying relationship between temerature variation versus difference between signal levels. What is difficult about that?
Could you recommend any experiments which could establish a thermal steady-state? I believe noise as well as music should be considered. Although I'm not sure how one would apply that in practice (music).
I'd be interested in gaining access to the resources of my University to conduct such a test.
It's not a deffinition. It doesn't nail down anything. Any time constant is possible, or no time constant - meaning steady state - etc. It simply does not quantitatively or qualitatively define the term.
Thermal steady state is reach when all parts that contribute to the sound radiation have reach a constant mean temeprature - there will always be variation about the mean with the signal. But at some point, the mean temperture of each part has come to a stationary value - the steady state. It would take a very long time for the magnet to come to this state, because the air in the box would have to reach steady state since there is a lot of convection cooling of the magnet by the air. The voice coil will reach a near steady state very quickly - by "near" I mean its mean value will approach a rate of change that has the same time constant as the magnet. But its temperature will fluctuate very rapidly about this mean dependning on the signal content.
Its an easy thing to model and to simulate audibly, but its the time constants that are difficult to get and without those the simulation could be way off or right on. As I said before, everything depends on the time constants.
You are considering how to mathematically calculate it. I consider actual testing measurment logging under realistic conditions. We just have our different ways.
Just wondering how fast your test set-up needs to be. You want to see the peaks and modulation from the drive signal not the average so you would have to sample at a rate faster than the rate of the temperature change. Just how fast does a wire heat up??
Using a light bulb as an example it seems it can be quite fast to heat up and takes time to cool off. Has anyone used a thermal imager on a light source to see what a filiment does using high speed imagery? Obviously not a voice coil but a good example of the rate of temp change in a piece of wire depending on power input. Could you get a fiberoptic probe into a speaker to "See" the voice coil temperature using a thermal imager??
Rob🙂
Using a light bulb as an example it seems it can be quite fast to heat up and takes time to cool off. Has anyone used a thermal imager on a light source to see what a filiment does using high speed imagery? Obviously not a voice coil but a good example of the rate of temp change in a piece of wire depending on power input. Could you get a fiberoptic probe into a speaker to "See" the voice coil temperature using a thermal imager??
Rob🙂
Hi Rob
I would sample at 48 kHz, of course. Thats easily fast enough to catch any thermal time constants.
The trick to what I do is to realize that the impedance is available with a tenth of a sec or less timing interval (Z(w) = V(w) / I(w)). From the impedance I can find Re, and from Re, I can find the VC temperature (I need to know the VC material of course). So I can track the VC temperature in time to about .1 sec resolution and maybe faster if I perform some signal processing tricks to speed up the calculations. But I am certain that .1 sec is easy and likely sufficient.
All I need are the voltage and current samples using a standard sound card. I don't even need to open up the system, I can do this with it unchanged. Of course crossovers pose some issues, but a driver feed directly from an amp is easy.
I don't need any sophisticated thermal equipment - just a PC with a sound card and MathCAD.
a FLIR high speed infrared camera may suffice.
It appears Dr. Shin (Purdue University) has access to a FLIR SC3000 Infrared Camera.
ThermaCAM® SC 3000 Infrared Camera - FLIR Systems
It is able to operate at 900hz NTSC / 750hz PAL
Would that be sufficient to capture the dynamic temperature shift?
Interesting😀
Although, as I'm sure you're aware, further experimentation would be required to properly elucidate the time constants of the various other parts of the magnetic structure.
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Dr. Geddes,
Let us assume we have 5 square copper blocks of variable depth and 5 square aluminum blocks of variable depth and equal area to the copper blocks. The blocks are then stacked randomly. A heat source is connected to the bottom of the structure and a measurement device is connected to the top of the structure.
Due to the multiple thermal interfaces, could we not describe the heat flow through the structure as changing with time. I believe an analog can be taken to velocity. If a system possesses a non-constant velocity, could we not describe it as possessing an *acceleration*?
I assumed an ESL with a height of 2m listened to at a distance of 4m and ear at 1m above the floor, ceiling height 2.4m and calculated the delays for the signal from the top and the first reflections from the ceiling and floor (compared to the direct signal from the mid of the panel).
top of esl: 3.6e-4 (s)
floor: 1.3e-3 (s)
ceiling: 2.5e-3 (s)
OK maybe not exactly same order. The question is will the ear/brain interpret a delay of 400 us in a different way than a delay of 1300us? I would really like to know if this spread of arrival times from a large transducer is an audible problem or not. And if so, how large can the spread be before it becomes audible.
You and Earl seem to agree on the books to read, thanks to you both for your recommendations. Time to order some books.
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