HI John
But I think that it is important not to allow false statements to stand. They get propagated and expanded into the highly erroneous dogma that plagues audio. Opinions of "quality" can be anything, but physical facts need to be corrected.
But I think that it is important not to allow false statements to stand. They get propagated and expanded into the highly erroneous dogma that plagues audio. Opinions of "quality" can be anything, but physical facts need to be corrected.
Maybe I just keep using the term improperly. For me to "do the work" means to do a positive work (on something), i.e. to loose energy. Not for the whole system, but for a part of it (be it a bullet or a piston). I have never even thought about loosing any energy in total.
- I would like to thank Geoffroy again, for he was really helpful for my better understanding. And I guess it's the right time to leave it at there 🙂
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As Earl said, energy can not be lost or created, but simply transferred.
Whenever work is done against an opposing force, energy is transferred.
Consider dragging a heavy box at steady speed over a rough surface. The work done by your muscular force against the frictional force transfers energy in your chemical store to heat energy (kinetic energy of molecules).
Consider lifting a heavy weight at a steady speed. The work done by your muscular force against the gravitational force transfers energy in your chemical store to energy stored in the gravitational field (gravitational potential energy).
Now consider forcing a loudspeaker cone to oscillate at a steady frequency. The work done by the magnetic driving force against the restoring force of the suspension transfers energy to heat while the work done against the damping force of the air transfers energy to sound energy.
A significant amount electrical energy is converted to heat in the voice coil so that the conversion of electrical energy to mechanical energy is less than 100% efficient.
The subsequent conversion of mechanical energy into sound is extremely inefficient.
Whenever work is done against an opposing force, energy is transferred.
Consider dragging a heavy box at steady speed over a rough surface. The work done by your muscular force against the frictional force transfers energy in your chemical store to heat energy (kinetic energy of molecules).
Consider lifting a heavy weight at a steady speed. The work done by your muscular force against the gravitational force transfers energy in your chemical store to energy stored in the gravitational field (gravitational potential energy).
Now consider forcing a loudspeaker cone to oscillate at a steady frequency. The work done by the magnetic driving force against the restoring force of the suspension transfers energy to heat while the work done against the damping force of the air transfers energy to sound energy.
A significant amount electrical energy is converted to heat in the voice coil so that the conversion of electrical energy to mechanical energy is less than 100% efficient.
The subsequent conversion of mechanical energy into sound is extremely inefficient.
The "restoring force" cannot dissipate energy, it stores the energy as potential energy, returning it back to the mass as kinetic energy, rinse, repeat. There are frictional losses in the suspension, but these are usually small, maybe 5%. The vast majority of loss occurs in the voice coil winding as heat.
I asked this very question, i.e. what difference does the absence of air make, but as my question was regarded silly, I didn't ask again... 🙄
Correct! I'll retract that and say that work done against the resistive forces of the suspension transfers energy to heat. Thanks!
Are these modes completely sufficient to fully decompose the boundary conditions? I checked out this link and it seems that they are. However, this page refers to the linearized Euler equation which is for inviscid flow, if I recall correctly. Doesn't vorticity require viscous forces to propagate in a fluid? Hence, isn't viscosity also needed for vorticity waves to exists? I might have to do a closer reading.
I have only worked with hydrodynamics from afar, like when, say, you derive the Navier-Stokes equation using statistical mechanics. As such, I haven't worked so much on solutions. It does not surprise me, but I wasn't aware of the entropy wave. Thank you. At first, I thought you were referring to shock waves which are not really waves.
I agree with the meaning, but dissipation is usually not taken to mean disappearance, but rather taken away from the system of interest. Of course energy is globally conserved!
If you were referring to my posts, then what I said was the electrical to mechanical transducer is efficient as a mechanical motor. The inefficiencies only arise when one attaches a mostly reactive load on that motor. Then, as the energy is reflected by the load it can only be dissipated in the motor itself or in the source. So, I wouldn't say that the electro-mechanical system is inefficient but rather that the acoustical-mechanical system is. Take a standard electrical motor with nothing on the spindle. Electrical motors are in general extremely efficient. However, if I take the output to be the motion of the air around the spindle, then, of course, almost all the energy is dissipated in the motor itself, but the input power can be (dependant on motor type) comparatively small compared to the motor full rated capacity as the motor do almost no work beyond heating itself. If I now attach a fan to the spindle, I load the motor with a resistive load and the efficiency drastically increases.
In both cases, I wouldn't say the motor is inefficient. However the entire system is.
By the way, I want to thank you for that book "Audio transducers". Some parts where really helpful when coding my simulations.
I'm still not completely on-board with this. If 95% of the energy is dissipated in the electromechanical system then how can it be efficient unless the system that you are discussing is electrical to thermal, which is very efficient, but electro to mechanical is not. If I can somehow load the mechanical system with a fluid impedance comparable to the impedance of the mechanical system then I can get about 50% efficiency at best. Hence best case the mechanical system is only 50% efficient. I am not an electric motor expert so I don;t know how to compare them to a loudspeaker other than to understand that in a motor 100% of the turns ratio is magnetically coupled. In a loudspeaker it is far far less - more wire is outside the gap than inside. I think the motor/loudspeaker comparison is going to be misleading.
Does an increased mag field really increase the efficiency? Lets take a theoretical driver thats 100% efficient, if we double the mag field it cant increase the efficiency.
That is at maximum power transfer. If the impedance of the load is much higher than the source, then the efficiency can easily go beyond 50%, albeit with a lower output power. Your comment about motor is true in the sense that a loudspeaker motor is usually not optimized for efficiency, but underhung coils can circumvent this issue. In any case, it remains that while speaker motor are a less efficient than industrial motors, they remain surprisingly efficient machines.
My main point was that the system efficiency can be low while still including efficient subsystems. This is the case for the electrical to mechanical transducer in a speaker.
To further illustrate this point, consider the case of a system that raises a weight (the output work) using electrical input. Suppose at the input is a standard transformer, amongst the most efficient machines constructed by humans. The output of the transformer could drive a high impedance motor resulting in a very efficient system. However if the motor windings impedance is much lower than that of the transformer, then a system with abysmal efficiency results, with most of the losses in the transformer itself. One could then say that the transformer used in this configuration is then quite inefficient, which would be true. However, and it might be an abuse of language to do so (I'm not a native anglophone after all 😉), when ascribing efficiency to a subsystem, I tend to consider only the inevitable losses and not those caused by impedance mismatch, which I ascribe to the total system. The reasoning behind this is that some process are simply inefficient, irrespective of the system they are used in. For instance, all the thermodynamic cycles suffer from a fundamental limitation on their efficiency caused be the associated creation of entropy.
To conclude, I agree that at some point, this becomes a debate of semantic, but I think the above example conveys my view point well enough.
Regards,
Geoffroy
If speaking about acoustical radiation efficiencies, a bit, yes, but that will mostly push the losses elsewhere, like in the power supply itself. You simply can't drive a low impedance load (air) from a high impedance source (the rest of the system) efficiently without a transformer between the two.
When one talks of superconducting coils, the usual assumptions of negligible source impedance does not hold. Likewise for the mechanical losses of the suspensions.
If you are decelerating a mass with your hands, it is indeed doing work on you and not all that energy is transformed as heat (that would violate conservation of momentum), some kinetic energy will be transferred to you (and the Earth you stand on). The exact amount depends on many factors which starts to get beyond what fits in a forum post: one must consider the type of collision (elastic/inelastic) as well as be careful with the reference frame one works in.
As a simple case, suppose you are floating in space, at rest in an inertial frame of reference, and that the mass m weighs as much as you and is being thrown towards you with velocity v. Total momentum must be preserved. As the initial momentum is p0=mv and the final object (you + the mass) has mass 2m, one has that the final momentum pf = 2 m vf = m v => vf = v/2. The kinetic energy before is 1/2 m v^2 and after it is 1/4 m v^2. So, half the initial value. The rest of the energy is dissipated as heat in the mass and your body.
Concerning the heat in the muscle, this is yet another phenomenon. The heat dissipated by muscle does not vary much with the actual work done. (You don't get cooler when lifting stuff!) This heat is simply a byproduct of how muscles function. It is a thermodynamic cycle that produces entropy and, as such, must have waste heat, like a steam or gasoline engine. It is interesting to note that this concern is not present for devices such as most electrical motor, transformers, and hydro-power turbines, explaining their potentially really high effiencies. Entropy is a really hard concept to grasp fully and frankly, most presentations are just misleading or plain wrong. Concretely, it implies that some forms of energy are of higher "usefulness" than others, where usefulness is to be understood in the sense of work you can do with it. Heat is essentially the least useful form of energy, while gravitational potential energy and electric potential, amongst the most useful.
I should stop now as this will become a physics class! 🙄
Regards,
Geoffroy
The Navier-Stokes equations are nonlinear and can be expressed in a range of forms. The primitive form use 3 velocity components and 2 independent thermodynamic variables (quite a few choices) expressing the conservation of mass, momentum and energy hence the 5 waves. The decomposition into an average part and an oscillation about that average part can also be done in a number of ways. This makes sound a mathematical construct that is ambiguous in the presence of other waves which surprises some.
I think there is still a prize of $1 million for proof on the existence of solutions to the Navier-Stokes equations. It is one of the unsolved biggies in mathematics.
Vorticity is the amount a fluid is spinning and involves only gradients of the velocity field. It is independent of whether particular forces such as that due to viscosity are present.
Entropy waves are only significant in the presence of significant temperature gradients so perhaps a registerable amount around a hot voice coil but negligible elsewhere. They have a more important role in processes like combustion and possible interactions with sound waves creating instabilities.
If you decompose the flow into an average part plus waves then vorticity waves will generally contain most of the energy in low Mach number flows. For example, if you consider an oscillating woofer in a ported cabinet almost all the motion inside the cabinet, through the port and in the shear layers and entrainment outside are vorticity waves not sound waves. Sound waves move at the speed of sound whereas vorticity and entropy waves move more slowly around the speeds of the mean flow. We will leave it as an exercise for the OP to determine how much energy is in the sound waves and how much in the vorticity waves.
Relationships of physical variables need not be necessarily linear. For instance, the force acting on a mass m due to a celestial object of mass M with their centres of mass separated by r is:
F = GmM/r^2 {G is Newton's constant of gravitation}
The same can be said about kinetic energy which is not linear. Doubling the velocity of an object does not double its kinetic energy: the kinetic energy is quadrupled instead.
Thank you for the answer. That prize is still there. Fun anecdote: a professor in the same building I work in bumped into me in the hallway and asked me what I thought about a detail in an attempt at a solution. He then told me to keep it quiet as he is competing with colleagues... Not the best attitude, but it was funny.
Didn't vorticity involves curl of the velocity field? I know it can be present without viscosity, but can it propagate without it?
Of course. But since F is directly proportional to B it would seem linear, no? Twice the B means twice the F and twice the cone acceleration, twice as efficient or is output power not linear with speaker F (a). Wheres the catch? So does anyone know the actual relationship between the magnetic field and speaker efficiency?
I dont think your definition of efficiency including the source is very standard. Ive never seen a motor spec for efficiency that depends on source impedance.
So if we are just talking about a perfect speaker with no coil resistance no brekup or cone deformation and no spider/surround where does the lost energy go? And would this not set the upper limit for speaker efficiency?
The guy in this link seems to know!
Loudspeaker Technology Part 12: Speaker Efficiency - The Broadcast Bridge - Connecting IT to Broadcast
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