Speaker "Speed"

[Holmz]

Unfortunately, you're betrayed by AI. You can run a dimension analysis, without needing anything knowledge of acoustics, and see that AI was giving you wrong info.
The dimension (unit) of the quantity inside the log₁₀ operation must be unit-less (as it must be a ratio). But AI gave you a formula that resulted in a dimension of L (length), and therefore oops.
View attachment 532773

The correct formula is this. You can substitute U₀ = π a² v⟂ (volume velocity = piston area × velocity normal to surface) into the correct one and find out that the AI formula had an extra "a" (piston radius) in the numerator and the 4π below should be 2π.
View attachment 532778

I think that we can pretty much ignore the Bessel function and the angles; as most common sized subwoofers and the frequency range over which they play, result in “not a great deal of directivity”.

 

[Newman]

I've read about it many times but was never sure if it's true
As an example, would a 10-inch woofer always be slower than a 6.5-inch woofer?

Does my 2-year-old post earlier in this thread, copied from my post 4 years ago in a different thread, still help with your question?

 

[dfuller]

Does my 2-year-old post earlier in this thread, copied from my post 4 years ago in a different thread, still help with your question?

Don't kid yourself man, he's completely lost in the sauce.

 

[Waveform Fidelity]

Unfortunately, you're betrayed by AI. You can run a dimension analysis, without needing anything knowledge of acoustics, and see that AI was giving you wrong info.
The dimension (unit) of the quantity inside the log₁₀ operation must be unit-less (as it must be a ratio). But AI gave you a formula that resulted in a dimension of L (length), and therefore oops.
View attachment 532773

The correct formula is this. You can substitute U₀ = π a² v⟂ (volume velocity = piston area × velocity normal to surface) into the correct one and find out that the AI formula had an extra "a" (piston radius) in the numerator and the 4π below should be 2π.
View attachment 532778

I should have got my old books on acoustic out and read them! Now I am curious to where the cited equation originated.

 

[Newman]

See? As soon as people start quoting AI, suddenly the thread is diverted into fact checking AI, examining AI's sources, etc.

 

[Newman]

That's why it's best to follow the ASR site policy on using AI in posts, which wasn't followed in this case:

1. If you are going to use AI, make it absolutely clear up front before just copying and pasting AI content.

2. Show the prompt you used and the engine (ChatGPT, etc.). Both of these can be useful to understand how the answer came about.

3. Please, please be mindful that you are dealing with combination of AI technology+the company behind it, wanting you as a customer for life to monetize. The latter will attempt strongly to give answers compatible with what you are asking so you don't go away unhappy. In other words, AI on controversial topics, is likely to give you the answer you want to hear than an unbiased statement.

4. AI cannot be your sole post and certainly not the thread starter. You can use it as part of your post but not the entirety of it. Such threads will likely get reported and deleted by us.

5. Personal advice: you need to know as much about the topic as the AI. Otherwise, you won't know if it is telling you the truth or not!

6. The Master AI thread is excluded from such rules.

7. I am in arguments on another forum and surprisingly, AI has been elevated as authoritative source! Often it is the only counter answer given. We won't be going there here.

 

[Waveform Fidelity]

See? As soon as people start quoting AI, suddenly the thread is diverted into fact checking AI, examining AI's sources, etc.

Why do you think it was AI generated?

 

[Waveform Fidelity]

Does my 2-year-old post earlier in this thread, copied from my post 4 years ago in a different thread, still help with your question?

Don't kid yourself man, he's completely lost in the sauce.

That’s the thing with myths…. no matter how many facts and explanations are provided, the topic never concludes. Its a bit like convincing flat-earth believers they have it wrong. I had a colleague that believed a satellite few in an orbit based upon “aerodynamic flight” no amount of quoting Keplers law of motion, or pointing out the was a lack of air in space would change his mind, so I asked the orbital mechanics team to talk to him…. They gave up as well.

 

[Holmz]

You don't need that force. The current in the voice coil combined with the magnet (together the motor) brings it back. It doesn't just hang around waiting for the "spring" part of the spider to pull it back.

Let’s say that the current was at some value and drops instantly to zero.
What is restoring back to the centre, when there is no current?

 

[antcollinet]

Let’s say that the current was at some value and drops instantly to zero.
What is restoring back to the centre, when there is no current?

How will the current drop instantly to zero? The voltage might, but as long as the voice coil is moving, there will be back EMF creating current.

But yes - I have thought more about it since then. What I am not clear on is:

Surely the spider does something to move the cone towards the centre because it is a spring as well as a damper. But how significant compared with the motor, while a signal is driving the voice coil? If a sine wave is being generated, then surely it is not the case that the acceleration from the motor is only during the rising voltage - and while the voltage is falling, only the spider pulls it back, because at the peak of the wave from the cone is moving fastest - back EMF is greatest, and the reversal of voltage below the back EMF reverses current flow and "motors" the motion back towards the centre.

(I am analogyising the behaviour of an electric induction motor in acceleration/deceleration mode - but don't really have a clear mental model of how it translates to speaker drivers)

 

[Holmz]

How will the current drop instantly to zero? The voltage might, but as long as the voice coil is moving, there will be back EMF creating current.

But yes - I have thought more about it since then. What I am not clear on is:

Surely the spider does something to move the cone towards the centre because it is a spring as well as a damper. But how significant compared with the motor, while a signal is driving the voice coil? If a sine wave is being generated, then surely it is not the case that the acceleration from the motor is only during the rising voltage - and while the voltage is falling, only the spider pulls it back, because at the peak of the wave from the cone is moving fastest - back EMF is greatest, and the reversal of voltage below the back EMF reverses current flow and "motors" the motion back towards the centre.

(I am analogyising the behaviour of an electric induction motor in acceleration/deceleration mode - but don't really have a clear mental model of how it translates to speaker drivers)

Just try not to think of voltage… And I also find it helpful not to think of sine waves.

If the current is in the positive sense then the magnetic field is applying a force in one direction.
The force will result in the cone remaining to go in that direction until it hits the stops, or until the suspension forces equal the motor force.

If/when the current goes to zero, then maybe it is the surround and the spider providing suspension that brings the cone back to the middle.
It is probably one of the TS parameters that describes it.

Probably as much, or more of an EMF generator, would be any mass of air in the port which would keep providing some more intertia to help suck the cone along.

Back to the sinewave… The motor drives it outwards for a positive current, and then on the negative voltage/current side of things the sinewave of the motor is “driving” the cone towards the back of the cabinet. SO it is always pushing and pulling the voice coil “going both ways”.
If there was no surround (no suspension) then it would be driven to-n-fro solely by the motor.
Which is sort of the reason when subs should not be played below some minimum frequency which is an even greater issue for a ported sub being played below its unloading frequency.

 

[antcollinet]

And I also find it helpful not to think of sine waves.

But I think we must. DC currents don't exist when listening to music, and zero current only exists as a crossover from positive to negative and back. And the cone is always in motion. This is when relative influence of spider to motor is relevant.

Only when we press stop, and voltage falls to zero and currents decay does the spider become unambiguously dominant in returning the cone to centre.

The DC behaviour is simple to understand. Current equals force. When motor force is equal and opposite to spider force, then a position is defined (assuming end stops not reached).

But this situation never arises during listening. Sometimes the motor will oppose the spider - at other times the motor force will be in the same direction as spider force.

I'm guessing it is possible to model with an equivalent circuit. One day when I have the time I'll try to find one.

 

[BassTinker]

How will the current drop instantly to zero? The voltage might, but as long as the voice coil is moving, there will be back EMF creating current.

But yes - I have thought more about it since then. What I am not clear on is:

Surely the spider does something to move the cone towards the centre because it is a spring as well as a damper. But how significant compared with the motor, while a signal is driving the voice coil? If a sine wave is being generated, then surely it is not the case that the acceleration from the motor is only during the rising voltage - and while the voltage is falling, only the spider pulls it back, because at the peak of the wave from the cone is moving fastest - back EMF is greatest, and the reversal of voltage below the back EMF reverses current flow and "motors" the motion back towards the centre.

(I am analogyising the behaviour of an electric induction motor in acceleration/deceleration mode - but don't really have a clear mental model of how it translates to speaker drivers)

The question you are asking about the spider/suspension is a good one because the answer is a long one.

As you mentioned the spider, I can already tell you right away: the spider has no big influence on the stiffness behavior of the driver as it is dominated by the suspension. The spider is mostly there to keep the voice coil in the center of the air gap, but radially seen. So basically it prevents the voice coil cylinder to hit the ferromagnetic material at the air gap. Electrodynamic headphones transducers usually dont even have a spider.

You are completely right about the back EMF when looking at the voltage response of the driver. The velocity of the cone creates a back EMF inside the voice coil, resulting in a current generated in said voice coil. This back EMF slows down the movement towards the resting position and can be observed in the current of a step response ("instantly turning off the DC voltage") of a transducer.
Now coming to suspension, we imagine the following case: at first, there is no current flowing through the transducer. Then, we apply a DC current to it, basically generating a "step" in the current flowing through it (see Figure below, I is the current in amperes, X is the displacement measured with a laser in milli-meters). Important: It has to be DC current, not voltage, because the current directly controls the force on the diaphragm!

As we can see in the above Figure, the displacement is not instantly moving to a fixed displacement, but "slowly approaching" a displacement value. I had to make a logarithmic x-axis because otherwise, this effect is hard to observe. This effect is called the "creep effect" and is an inherit property of the suspensions material. I wont get too deep into this, but you can find out more if you look for "relaxation and retardation times of materials". This effect can also be described as a time-dependency of the stiffness K, as its value changes at the displacement over time. If we translate this to the frequency domain - we now have a frequency dependency of the TS parameter K, so it is actually K(f).

The frequency-dependency of the stiffness visualizes one thing - the question "which of the two factors - magnet system or suspension - is more dominating" is actually a question of frequency. To keep it short: the prominent region of stiffness effects is in the low frequency range, therefore also often called "stiffness controlled region". The region of the inductance frequency-dependency (and also non-linearities, concerning the mentioned back EMF effect) is most dominant in the high frequency region.

Have in mind - we are only talking about linear effects here. Not to be mixed up with non-linear behavior. Even though they all play together at the end, they should be looked at in a seperate way.

 

[Holmz]

But I think we must. DC currents don't exist when listening to music, and zero current only exists as a crossover from positive to negative and back. And the cone is always in motion. This is when relative influence of spider to motor is relevant.
…

I think that the spider/surround forces are pretty low in comparison to the motor force.

…
I'm guessing it is possible to model with an equivalent circuit. One day when I have the time I'll try to find one.

I think it would be easier to approach it as a simulation/model.
Then every say 1 millisecond (or 1/10), just assume that the sampled voltage/current it constant, and plot derive the new position.
Wind the clock up to the next sample time and repeat.

We have force, so we know pressure and SPL.
And if we know mass and the air mass, then we know the cones new position.

 

[BassTinker]

I have posted a quite extensive answer, but apparently it takes some time to be approved by moderators. It was public already, but after a short edit, it seems to require mod approval again....when its approved, then you will have some answers to the questions here.

EDIT: Ah, there you go. See my post above the last one from @Holmz

 

[Holmz]

Now coming to suspension, we imagine the following case: at first, there is no current flowing through the transducer. Then, we apply a DC current to it, basically generating a "step" in the current flowing through it (see Figure below, I is the current in amperes, X is the displacement measured with a laser in milli-meters). Important: It has to be DC current, not voltage, because the current directly controls the force on the diaphragm!

As we can see in the above Figure, the displacement is not instantly moving to a fixed displacement, but "slowly approaching" a displacement value. I had to make a logarithmic x-axis because otherwise, this effect is hard to observe…

Can you also show a linear x axis section just in the range where the when the current starts. I think it is around X=0.25?

 

[Waveform Fidelity]

The question you are asking about the spider/suspension is a good one because the answer is a long one.

As you mentioned the spider, I can already tell you right away: the spider has no big influence on the stiffness behavior of the driver as it is dominated by the suspension. The spider is mostly there to keep the voice coil in the center of the air gap, but radially seen. So basically it prevents the voice coil cylinder to hit the ferromagnetic material at the air gap. Electrodynamic headphones transducers usually dont even have a spider.

You are completely right about the back EMF when looking at the voltage response of the driver. The velocity of the cone creates a back EMF inside the voice coil, resulting in a current generated in said voice coil. This back EMF slows down the movement towards the resting position and can be observed in the current of a step response ("instantly turning off the DC voltage") of a transducer.
Now coming to suspension, we imagine the following case: at first, there is no current flowing through the transducer. Then, we apply a DC current to it, basically generating a "step" in the current flowing through it (see Figure below, I is the current in amperes, X is the displacement measured with a laser in milli-meters). Important: It has to be DC current, not voltage, because the current directly controls the force on the diaphragm!

View attachment 533334

As we can see in the above Figure, the displacement is not instantly moving to a fixed displacement, but "slowly approaching" a displacement value. I had to make a logarithmic x-axis because otherwise, this effect is hard to observe. This effect is called the "creep effect" and is an inherit property of the suspensions material. I wont get too deep into this, but you can find out more if you look for "relaxation and retardation times of materials". This effect can also be described as a time-dependency of the stiffness K, as its value changes at the displacement over time. If we translate this to the frequency domain - we now have a frequency dependency of the TS parameter K, so it is actually K(f).

The frequency-dependency of the stiffness visualizes one thing - the question "which of the two factors - magnet system or suspension - is more dominating" is actually a question of frequency. To keep it short: the prominent region of stiffness effects is in the low frequency range, therefore also often called "stiffness controlled region". The region of the inductance frequency-dependency (and also non-linearities, concerning the mentioned back EMF effect) is most dominant in the high frequency region.

Have in mind - we are only talking about linear effects here. Not to be mixed up with non-linear behavior. Even though they all play together at the end, they should be looked at in a seperate way.

This is very interesting and not would one would expect or easily observe, or look at from a practical user case. It sounds like you have precision tools to be able to measure the cone position. I’d be interested in learning more about the non-linear effect of the suspension/spider system and how a practical suspension system varies from the theoretical one. For example, can you observe/measure very small movement for very small currents? Does the current vs displacement curve pass through zero, or is their some hysteresis? Is there a minimum force that is needed to make the cone move from its rest position? Many thanks!

 

[Holmz]

This is very interesting and not would one would expect or easily observe, or look at from a practical user case. It sounds like you have precision tools to be able to measure the cone position. I’d be interested in learning more about the non-linear effect of the suspension/spider system and how a practical suspension system varies from the theoretical one. For example, can you observe/measure very small movement for very small currents? Does the current vs displacement curve pass through zero, or is their some hysteresis? Is there a minimum force that is needed to make the cone move from its rest position? Many thanks!

I know you’re not asking me, but…

The fact that the damned things make sound with the volume knob twisted just a fraction above zero, indicates that the cone must be accelerating.
And if the distortion is low, then it infers that it is remaining linear, and not sticking like a slip-stick oscillator.

There is some motor hysteresis “in the magnet I think”, according to some Bruno paper that was worth a read.

 

[Waveform Fidelity]

Well, yes. Intuitive reasoning is all very well, but how in your scenario how would you know? Rotating your volume knob will bring the loudspeaker to life, but what’s happening before that? By the time you hear it it is of course in free motion. If you placed your ear next to the diaphragm, reduced your volume, and repeated the same test, again you would hear it when it was moving. In this experiment you could keep reducing the volume until you reach the threshold of hearing, but at this threshold level there is no way the ear is going to detect distortion, so you have to use instruments.

It sounds like BassTinker has a laser tool that detect the motion of the cone, so I’d be very interested in seeing what happens when the cone just starts to move caused by the minimum current. Of course this will be very different for a woofer and tweeter as the compliance of the suspension systems are very different.

In the DC current step, it is unexpected that even after the DC current is held constant, the cone “creeps out” further over 10’s of seconds? Because the suspension system resorting force is somehow reducing? I find that very interesting

 

[bmc0]

There is some motor hysteresis “in the magnet I think”

It's in the iron rather than the magnet.

And if the distortion is low, then it infers that it is remaining linear, and not sticking like a slip-stick oscillator.

Yes, exactly. An acoustic measurement will show the effect of "steppy" motion to well below the limits of audibility; no need to use a laser vibrometer.

In the DC current step, it is unexpected that even after the DC current is held constant, the cone “creeps out” further over 10’s of seconds?

This effect is well known and there are a number of papers about it. Here are a couple that aren't paywalled: 1) Loudspeaker Simulation considering Suspension Creep, and 2) Analyzing the Nonlinear Performance of Miniature Loudspeakers in Consideration of the Creep Effect. Creep is also mentioned in several Klippel papers and application notes.