Your question would be a nice one to see if a student really understands speakers, physics and the Thiele/Small parameters. Conservation law says no energy comes from the magnetic field. Equally the claims of increased efficiency miss the point. First consider the speaker response where the mass of the cone dominates, ie below the rise in impedance due to voice coil inductance and above resonance (below which the stiffness of the suspension controls the motion. Even better, an idealised version with a friction-less seal rather than a surround. The impedance seen by the amplifier looks like a capacitor (this is the down slope above resonance on a real speaker). This impedance is due to the mass of the cone system, reflected by the interaction of the voice coil movement and the field. It is proportional to the mass and inversely proportional the (BL)^2. So if you double the mass the capacitance doubles, but you have assumed double the BL too, so the resultant capacitance decreases by half. So the impedance has doubled. To maintain the same current, as assumed, the potential must double too. So same current, double volts = twice the power in, to provide twice the energy to the cone. Simple.😉 A bit harder to analyse once you include VC resistance but the principle is the same because the system is linear .
Best wishes
David
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Well, the "reference efficiency" to the acoustic side stays the same for the whole speaker (for Bl and m higer in the same ratio). So no more power in for the same acoustic power out. But still the energy put into the cone motion is higher in the second case. So there must be less of heat and more of mechanical motion energy. That would make sense to me but I still don't understand how that really happens.
Or, what does this equation for "efficiency" really mean?
- Sorry, it's just not that easy for me 🙂 Maybe I just don't really understand the physics involved...
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Although I suspect you are not fully on top of the forms of energy present and the role of impedance in determining the amount of energy transferred between the different forms having reread your posts I think the first thing that is tripping you up is "With the same current", "For the same current",...
In your problem some quantities are fixed/known/imposed/constant and some need to be worked out in terms of quantities that are fixed/known/imposed/constant. Quantities like Bl and m are known. Quantities like F, I and a are not and need to be worked out in terms of quantities that are known. So you need to supply more information in order to determine the current which is what I was doing in my first reply as were one or two others in this thread.
There are a fair number of reversible and irreversible forms of energy present in a speaker driver but prior to tackling this I think you need to formulate the question more precisely. Although knowing the current cannot be imposed when a conventional constant voltage amplifier is driving the speaker may have answered it for you.
Andy, all you are saying is "you would understand if you knew it all (like me)". That I know too 😱 But thanks anyway.
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Not really and I looked up part of a post earlier in a text book which is an option open to you as well. I used an old paper text book bought when I was an undergraduate many decades ago but there are a number of stolen pdfs of current acoustic text books available on the web if you look.
I am saying you first need to formulate the right question to get the answer you want. Your opening question incorporates parts of an incorrect answer. When it comes to independent research working out what you don't know/understand is often more of a challenge than getting the answer when you have worked it out.
I am saying you first need to formulate the right question to get the answer you want. Your opening question incorporates parts of an incorrect answer. When it comes to independent research working out what you don't know/understand is often more of a challenge than getting the answer when you have worked it out.
Mabat, Andy is trying to tell you that in order for a calculation to be of some significance in understanding what is going on, you should first model both of your drivers. You said one has double the moving mass and motor strength. This changes impedance profile of each driver. For instance like this. The red curve is the one with twice the Mms and Bl.
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Of course I can do this and have done this, but without an explanation, it doesn't tell you much. And this is just the magnitude. So let's talk about the point where the magnitudes are the same - which is approx. at 200 Hz in your picture. Is the phase between the voltage and the current different? It is, I can tell you that, but why exactly? At 200 Hz the heavier cone will move with twice as big kinetic energy at its maximum speed. The current will be the same - at least its magnitude. And it's the current magnitude that determines the motion of the cone, right? ...
Maybe a better way of analyzing this would be in the time domain. I don't know.
Maybe a better way of analyzing this would be in the time domain. I don't know.
Hi,
The energy required to move the cone and to radiate sound is fully taken from the electrical input signal. It consists of a current and a voltage:
Source: Speaker equivalent circuit / electrical model | Audio Judgement
If Bl is doubled and v stays the same, then e doubles as well and hence, twice the energy is taken from the electrical input signal. 🙂
The energy required to move the cone and to radiate sound is fully taken from the electrical input signal. It consists of a current and a voltage:
- The current i is obvious, it's the voice coil current and also the input current.
- The voltage e is only a small part of the input voltage. It's the voltage induced by the velocity of the voice coil (back emf).
Source: Speaker equivalent circuit / electrical model | Audio Judgement
If Bl is doubled and v stays the same, then e doubles as well and hence, twice the energy is taken from the electrical input signal. 🙂
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I believe you are looking at this in a different way than what the OP had in mind. You are considering the efficiency of the driver (i.e., the acoustic output of the driver relative to the power input or voltage input to the driver). However, the OP question was about the energy conservation with respect to the kinetic energy of the moving parts of the driver (cone, suspension). The OP question also implied that the current is a-priori and artificially kept at the same value (not power, not voltage).
My view at this is as follows: if the moving parts take up twice the kinetic energy from the motor, the motor must take twice the energy from the amplifier (ignoring non-linear losses and stuff). At least this holds for instantaneous, non steady-state operation of the system. Yes, time domain might be important to consider (think steady-state sinusodial movement of the cone).
Hi,
so the energy needed to move the cone is given (i.a.) by a voltage induced by the cone velocity? But the coil stays still at the beginning. It seems we are all stucked 😕 🙂
But OK, I will look at the equivalent circuits (again). I guess it's all there, it's just that I don't see it. Thanks all for your effort.
The "forcing" on the electrical side is the difference between the voltage imposed by the amplifier and the back emf from the voice coil moving in the magnetic field. The back emf opposes the motion of the cone it doesn't drive it. The voltage from the amplifier is doing the driving.
Yeah, I get it. If I should re-phrase my not-understanding, I would write this:
The efficiency to the acoustic side stays the same for the whole speaker (for Bl and Mms made higher by the same ratio). So no more power in for the same acoustic power out. But still the energy put into the cone motion is higher in the second case. So there must be less of heat and more of mechanical motion energy. That would make sense to me but I still don't understand how that really happens.
Is this question better now?
The efficiency to the acoustic side stays the same for the whole speaker (for Bl and Mms made higher by the same ratio). So no more power in for the same acoustic power out. But still the energy put into the cone motion is higher in the second case. So there must be less of heat and more of mechanical motion energy. That would make sense to me but I still don't understand how that really happens.
Is this question better now?
You would have to equalize both cases for the same SPL, but then the velocities will be the same. And because the overall efficiency stays the same, the input power will also be the same. The voltage and the current won't be the same because the impedance (as a complex quantity) is not the same. High above the resonance it will differ very slightly, but it seems this little difference is enough to do all the trick (because the dynamic loudspeaker is so inefficient in the first place).
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Ok, you have two steel balls. One has mass M. the other has mass 2M. You drop then off a 50ft tower. Both fall at the same rate due to the force of gravity. Both hit the ground at the same time, at the same velocity. The 2M ball has twice the kinetic energy as the 1M ball. How did that happen?
My point here is that the OPs question has nothing to do with acoustics. He is asking about the difference in kinetic energy due to the difference in mass.
Kinetic Energy – The Physics Hypertextbook
My point here is that the OPs question has nothing to do with acoustics. He is asking about the difference in kinetic energy due to the difference in mass.
Kinetic Energy – The Physics Hypertextbook
Yeah, exactly! So how did that happen? 🙂
And don't tell me they are not falling. That would Einstein say but I would no understand it. At least the heavier can make bigger damage.
And don't tell me they are not falling. That would Einstein say but I would no understand it. At least the heavier can make bigger damage.
Doubling the flux density will also double the back EMF induced in the coil for the same coil length. This means, you will need twice the initial voltage to drive the loudspeaker.
In your analysis you have to take into account, the fact that the moving speaker coil, has a huge air resistance, and actually transfers almost all energy being supplied to the coil. You cannot assume F = ma, with m being the cone's and coil's combined mass. In moving, a speaker's cone disturbes air molecules setting up a longitudinal sound wave.
In your analysis you have to take into account, the fact that the moving speaker coil, has a huge air resistance, and actually transfers almost all energy being supplied to the coil. You cannot assume F = ma, with m being the cone's and coil's combined mass. In moving, a speaker's cone disturbes air molecules setting up a longitudinal sound wave.
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Why do you think the efficiency is the same in your two cases?
If you double the forcing factor and the mass of the cone but keep the same suspension stiffness and damping the frequency response will be changed significantly. How is the electrical resistance and inductance of the coil to be changed? Different ratios of these also change the frequency response. Keeping the radiation impedance the same in both cases will also mean frequency response variations. Etc...
If you write down the equation of motion in terms of known quantities as a function of frequency it will answer your questions (the current isn't known in the equation in the OP).
That accounts for drivers as well ! It makes a difference whether you drop a 23" onto your feet or just some tiny 2" fullranger !!! 😉
Fun aside: One has to take into account that we have some form of pendulum here with energyy that is changeing between kinetic and potential energy. So only the acoustic radiation and the friction losses consume "real" power.
Regards
Charles
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