I think something has been left out. An analogy: if five HoneyCrisp apples weigh one kilogram, how much do 27 grapes weigh? (red grapes, if that helps. Another hint: the grapes were grown in Peru.)
I fear that an incorrect assumption has been made. That assumption is that the "constant" current in both cases is caused by the same or nearly the same driving voltage. That is not true.
The driving voltage must be increased if the same acceleration is to be maintained. The impedance of the electromechanical system has increased. Same current, twice the force is needed (more, actually. We have been ignoring the 8 ohms resistance of the speaker driver, superconducting suggestions to the contrary). I expect more than twice the voltage will be needed, in the messy real world. It would be the very devil to measure accurately.
Twice the voltage at the same current to drive twice the mass at the same acceleration seems to me to be total energy conserved.
Bringing the voice coil to rest is a wholly different issue. First, three forces are involved, not just one. The first is the restoring force of the suspension. The second is the restoring force of the air behind the speaker, the "acoustic suspension". The third is the EMF from the coil. Call it direct EMF plus "back" EMF, if that makes you feel better. If we could know enough about the speaker box, the suspension, the driving circuit, and the speaker driver itself, we could generate a voltage that would bring the cone to a dead stop at the rest position. That kinetic energy is not lost. It doesn't disapper. Instead, it is converted to heat. Some of the kinetic energy of the cone will be absorbed in various Resistances in the driving circuit. (That is Resistance with a capital "R", as opposed to "impedances"). Some of the rest will be spent in physical resistance in the suspension, and a very small portion in eddy currents in the air.
An infinite baffle on a speaker with no connections to the coil would be pretty close to a "pure" suspension environment. Air at sea-level pressure is pretty close to a vacuum, anyway, compared to the physical cone. Thump the cone in the center, and it will oscillate briefly, then stop. Most of the energy will be converted to heat in the soft suspension. A tiny amount will become sound, or else eddy currents.
My understanding of the motivation for acoustic suspensions in the first place was due in part to high resistance losses for physical suspensions.
I fear that an incorrect assumption has been made. That assumption is that the "constant" current in both cases is caused by the same or nearly the same driving voltage. That is not true.
The driving voltage must be increased if the same acceleration is to be maintained. The impedance of the electromechanical system has increased. Same current, twice the force is needed (more, actually. We have been ignoring the 8 ohms resistance of the speaker driver, superconducting suggestions to the contrary). I expect more than twice the voltage will be needed, in the messy real world. It would be the very devil to measure accurately.
Twice the voltage at the same current to drive twice the mass at the same acceleration seems to me to be total energy conserved.
Bringing the voice coil to rest is a wholly different issue. First, three forces are involved, not just one. The first is the restoring force of the suspension. The second is the restoring force of the air behind the speaker, the "acoustic suspension". The third is the EMF from the coil. Call it direct EMF plus "back" EMF, if that makes you feel better. If we could know enough about the speaker box, the suspension, the driving circuit, and the speaker driver itself, we could generate a voltage that would bring the cone to a dead stop at the rest position. That kinetic energy is not lost. It doesn't disapper. Instead, it is converted to heat. Some of the kinetic energy of the cone will be absorbed in various Resistances in the driving circuit. (That is Resistance with a capital "R", as opposed to "impedances"). Some of the rest will be spent in physical resistance in the suspension, and a very small portion in eddy currents in the air.
An infinite baffle on a speaker with no connections to the coil would be pretty close to a "pure" suspension environment. Air at sea-level pressure is pretty close to a vacuum, anyway, compared to the physical cone. Thump the cone in the center, and it will oscillate briefly, then stop. Most of the energy will be converted to heat in the soft suspension. A tiny amount will become sound, or else eddy currents.
My understanding of the motivation for acoustic suspensions in the first place was due in part to high resistance losses for physical suspensions.
I pointed that out in post #55. However, the situation is more complex, due to the BL also doubling.
It's not exactly the impedance of the source, but more precisely it's resistance. Accounting for source impedance when evaluating system efficiency is absolutely critical and otherwise meaningless! But standard or not is beside the point. You see, in your perfect speaker, ALL the losses will be in the source/wires. Ignoring the wires (let's make them superconductors too!) and the acoustical radiation (which will contribute a minute resistive term in the impedance), this is like putting a perfectly reactive load on the terminals of your sources. Therefore, while no energy will be transferred to the load overall, there will still be reactive currents that will dissipates energy insides the source.
I suggest to everyone confused by the above to review the following article.
Let us do a simple thought experiment:cbdb said:
Imagine technology being able to provide speakers with a magnetic field in the order of 1,000,000T.
The back emf induced in a coil subjected to such a huge magnetic field, would be so large, that the coil would only be able to vibrate with very small amplitudes, to keep the instantaneous speed sufficiently low for any current to pass. This means, with such a huge magnetic field, the speaker efficiency will be much much lower! If we extrapolate to an infinite flux density, the coil would remain motionless imparting zero audio energy to air.
You have to keep in mind air has a different physics compared to a coil which obeys electromagnetism. Air requires a diaphram to vibrate with sufficient amplitude and speed for sound waves to be efficiently generated.
From the point of view of the coil, whether it causes the generation of sound waves or not, is immaterial. What is important for the coil is its intantaneous back emf, the resistance and the instantaneous driving voltage.
This would lead to the equation:
v = e + ir, where v = instantaneous driving voltage, e = back emf, i = instantaneous coil current and r = resistance.
e can be rewritten as: πDNuB where D = diameter of coil, N = turns of coil, u = instantaneous velocity, B = flux density.
v = πDNuB + ir ....................... (i)
The instantaneous electrical power delivered is:
p = vi = i(πDNuB + ir)
=> p = iπDNuB + ri^2 ...................... (ii)
Now let us define the instantaneous acoustic power as:
S = f(u,A) where u = instantaneous velocity of speaker diaphram and A = diaphram area.
So:
Efficiency =[ f(u, A) / { iπDNuB + ri^2 } ]. 100%
A higher efficiency at a higher B would imply f(u, A) increases faster than iπDNuB.
I tried to find a formula for f(u, A) but couldn't find any relevant material.
Since, the variables are the efficiency, u and i, knowing the real formula for f(u, A), would permit you to plot a three dimensional chart which you can study for more details.
Vorticity is a transported quantity like mass, momentum and energy and unlike quantities like pressure. It is convected, diffused and accumulated. The presence of viscosity prevents the velocity gradients becoming infinite at the centre of a free vortex which, depending on what you are doing, may make things better behaved.
The plot below compares the effect of doubling B and doubling l for the 8" subwoofer in an infinite baffle that I showed earlier. Doubling l assumed the coil in the datum configuration was half the moving mass, the resistance and inductance was doubled and how a larger coil could now fit in the gap was ignored. Not surprisingly it looks like the easy way of increasing Bl might not work and we need to discover a new more powerful modestly priced magnetic material. (And that the design of a driver tends to get optimised for the magnetic and coil materials it is using). Note this was done very quickly without normal checking and so may contain errors.
Attachments
Poorly stated, sorry. I meant that when one makes false statements of "facts". I'll try and correct the statement not the facts.
Absolute rocket science, the mass is added on the dustcap and the inductance is added outside of the gap.
- Status
- Not open for further replies.