Drivers behave as a mass on a spring...

[Overkill Audio]

Hi All,

The purpose of this thread is to discuss the physical movement of loudspeaker drivers using cones, domes, ribbons, compression drivers and planar drivers.
The starting point is the ATTACHED DOCUMENT I wrote a few years ago, please have a read and let me know your views!

The two very different and seperate problems, that I would like to look at are :
(1) Cone / ribbon break up which is well documented and understood by 99% of audio folks..
(2) The much more fundamental and serious problem (in my view!) of the entire cone / coil/ spider / suspension ocillating out of control ie behaving as a "mass on a spring" AFTER (this is vital) the electrical impulse ( musical note) has stopped and no longer has any "grip" on the cone.
No matter how fancy the motor design.... It cant work when it is swithced off...!
The only reason I mention point (1) is to highlight that it is seperate to and diffrent from the second problem. "Mass on a spring" behaviour is the elephant in the room that I would like to focus on and explore.

Thanks in advance

Derek.

[Overkill Audio]

Hi All,

I thought it would be good to post Tom Danley's great reply to my document that he kindly posted in Bears thread.
Great starter for 10... Thanks Tom!

" Hi
I would agree with much / most of what you say, the differences being mostly a different way of seeing how the driver properties tie together.

How a loudspeaker driver works can be explained in great detail but rarely does one hear discussion of how sound works and what a driver really does. I like to say so far as size and time, sound is something like a set of Russian dolls, the traditionally smallest one (20KHz) only 5/8 inch tall while the largest at 20Hz is 1000 times large. You see this volume relationship with woofers, if you want the same sensitivity but an octave lower corner F, it requires you cube the volume not double it.
If you lower the corner frequency an octave but keep the size the same, the sensitivity goes down 9dB.

A lower frequency is larger in wavelength and naturally takes a longer time too.
For that reason, when looking at an event covering a wide bandwidth, time is often not a good frame of reference as the natural period for any event is directly related to frequency.
For example, some foam about subwoofer group delay without considering that any response feature always occupies twice the time if it happens an octave lower, that is to say a large GD is part of a low frequency response corner. In fact the phase response is locked into the amplitude response, any change in one causes the change in the other.
Conversely, a better way to view these things would scale the Russian dolls to the same size so that only deviations from the design are shown, like Cumulative burst decay or in wavelets. Here what would be ime is now related to the wavelength or period (like phase) for that particular frequency.
You thoughts about pistonic motion are mostly right, nothing in infinitely stiff so nothing is absolutely ridged. Conversely, when operating as a piston radiator, when a small fraction of a wavelength across, then the small amount of flex is averaged out as total displacement. In a high pressure design like some at work, the flexure of the cone is visible as an un-accounted for compliance between the horn and driver.

Cone breakup (and any other sharp resonance driven by the system) is really bad! Breakup magnitude relative to that below is sort of a radiator badness indicator.
The drivers motor is the primary distortion generator, the nonlinearity between the signal Voltage and motion. If one had a breakup that was say 20dB tall at 3KHz, then one might be tempted to think, ‘I can cross that out at 1500 with a 96dB /oct crossover and all is well. Yes, when you measure the response the effect of the breakup is not visible, cool!.

Do a distortion tracking measurement and you see that there is a large mound of 3rd harmonic at 1KHz, a similar mound of 4th harmonic at 750Hz and at every submultiple of the mound at 3K, that same resonant gain is applied to the existing motor nonlinearity and that harmonic and raise about 100X or 20dB.

When a woofer is acoustically small even what it does may not be obvious.
For example, what is known for sure is that if you put a microphone or pressure transducer inside a sealed box enclosure with a woofer mounted, one see’s that the internal pressure is directly related to the driver excursion at any frequency (where the enclosure is small compared to the wavelength).
In the range where one is in the box roll off (-12dB/oct) one finds that the driver excursion does not increase as the frequency falls, -12 dB per octave is a constant displacement slope.

Yet, if one monitors the internal microphone, one see’s flat response and a square wave in equals a square wave pressure what gives????
If you wanted such a woofer to produce a flat response externally, one needs to have the excursion increase by four times each time you go down an octave. This is to offset the changing radiation resistance which has a radiator size term relative to the wavelength look into radiator. With that requirement, what does the excursion look like required to produce a square wave now?
This is a constant acceleration response. Here it is the moving mass and the current to force transduction, in series with it’s Rdc makes it an acceleration device. That is why / how one can add mass to a given driver’s motor and NOT have an effect on it’s attack, speed of response step response or whatever measure of time one would apply. It is already controlled by mass, adding more only lowers the main resonance F and the efficiency etc. Conversely, the reason why large massive woofers do not respond quickly is because they have a larger motor which has more series inductance and this is what rolls the response off / slows its rise time.
Like the Russian dolls again, drivers can be suited to a frequency range, a big slow subwoofer driver maybe perfect doing that job even being slow because everything coming out of the low pass crossover IS slow.
You are concerned with an issues near to my heart, also the Manger is a driver I have had some time to play with and measure. In time response, it is the best driver I have ever measured, it occupies one point in time, over a very broad band and radiates as a simple source. AS you suggest it REALLY needs to be crossover over in the lower mid as it’s harmonic distortion skyrockets even at 1w @ 200Hz.

Understand what it does, it radiates a very simple portion of a sphere (read my other post about disappearing), it does that by producing a disturbance at the center which radiates outward at the speed of sound in air and then is absorbed. From that standpoint, it is conceptually similar to a Quad ESL-63 which constructs a portion of a spherical radaiton with sequential rings of ess radiators.
Our Synergy horns produce this also but by producing the high frequencies at the apex of a conical horn and progressively adding the mid and lower frequencies in time with the wavefront as it progresses forward (compensating for the order they emerge form the crossover) radiating a spherical segment that appears to have been from one source at the apex.

One thing that is required to act like a single source like the manger is the drivers acoustic phase must be around zero degrees over a broad band and the Manger does that and will reproduce a nice square wave. A woofer with flat response can’t do that until way above the low corner because of it’s acoustic phase.
Anyway, some random thoughts, time for turkey Phase II.
Best,
Tom "
__________________
Bring back mst3k and futurama

[planet10]

Originally Posted by Overkill Audio

The starting point is the ATTACHED DOCUMENT

Here is a pdf of the document for those that don't want anything to do with Word.

dave

[PbAg]

Hi Derek, I agree with your observations. However, consider what happens next, once the cone (piston) has started to move. The voice coil is now cutting through the magnetic field of the pole piece gap, and generating a voltage. The amplifier is meant to act as a short circuit to this voltage, which slows the cone right back down again.

Try this experiment: put a woofer (driver) on your desk. Tap the cone with your finger, listen to it "ring" like you predict. Now short circuit the two speaker terminals with a piece of wire. Try tapping the cone again. Notice the behavior is different? Very cool effect! - and fundamental to getting a speaker to behave.

[speaker dave]

Originally Posted by Overkill Audio

(2) The much more fundamental and serious problem (in my view!) of the entire cone / coil/ spider / suspension ocillating out of control ie behaving as a "mass on a spring" AFTER (this is vital) the electrical impulse ( musical note) has stopped and no longer has any "grip" on the cone.
No matter how fancy the motor design.... It cant work when it is swithced off...!
The only reason I mention point (1) is to highlight that it is seperate to and diffrent from the second problem. "Mass on a spring" behaviour is the elephant in the room that I would like to focus on and explore.

Thanks in advance

Derek.

Just to clear up one misconception, the motor does not turn off when the signal stops.

The motion of your mass on a spring is restrained near resonance by the combination of mechanical and electrical damping. Electical damping tends to be the stronger component and will be in effect as long as the low impedance of the amplifier is across the woofer. If a signal of some duration stops, the amplifier is not turned off, it is actively holding the output at zero volts.

Another interesting point is that the system only looks like a mass on a spring in the vicinity of resonance. Above resonance it looks like a driven mass and it would be hard to tell that the spring existed. Below resonance it appears to be a spring and the mass is not in evidence. At resonance we want to have the right amount of damping to control the motion and give the right bass level. Too little damping and the bass peaks and transient response suffers. Too much damping and the bass is weak.

David S.

[Conrad Hoffman]

An interesting exercise is to create a model for a given driver. You'll probably find that the values required to do so, at least for some frequencies, will be far beyond anything reasonable to assemble on the bench. It gives you an idea of the energy storage involved, not to mention the fun of making a bunch of impedance measurements. Nobody does it anymore, but a plot can be made using a y axis of reactance and an x axis of resistance. The plot will be circular near resonance, with points on the plot being specific frequencies.

[john k...]

Derek,

I don't mean to nit pick here but the initial description you gave in the write up not sufficient to begin to describe driver motion. I understand this is a first installment but to exclude damping at the start presents a misleading initial picture. Over most of a driver's operating range the spring effect, as well as damping, play little role in determining the driver's motion when a signal is applied. Second, while music may have sudden starts and sudden changes, it seldom has sudden stops. Music signals, even from a snare drum, are not impulses. Impulses contain all frequency components in equal magnitude. A snare drum whack will not contain any frequencies below that associated with the natural frequency of the snare drum skin as tensioned over the drum head. Additionally, a plucked bass guitar string or the skin on a snare drum is much more of an undamped oscillator than a typical driver. I understand that you have not yet introduced damping in your argument but to provide an initial description without such consideration of damping is inappropriate, IMO. Also, you fail to note that even in the case you sight the oscillatory behavior of the spring mass system after the signal is removed would be at the system's natural frequency which most likely has little or no relation to the frequencies contained in the initial drum whack. It is not an echo of the original.

When considering just a spring mass system, why not consider a mass suspended by a spring. Let's say we displace that mass a few inches and release it. I will oscillate at a natural frequency defined by the square root of the spring constant, K, divided by the mass, M. For the sake of argument let's call that fo. Now grab that mass with your hand and move it up and down very fast. Certainly you will have to over come the spring force but unless you displace the mass significantly and at low frequency, the most significant force will be that to accelerate the mass. Now all of a sudden release the mass. At the instant the mass is released it may have some displacement from its rest position or some velocity up or down (assuming motion only in the vertical direction), or both and the behavior of the system will be to oscillate at fo with an amplitude dependent on the displacement and velocity at the time of release, generally completely unrelated in frequency to the motion previously imposed on the system when hand held. Add damping and that motion will decay exponentially in time with or without oscillation, depending of the amount of damping.


When looking at the behavior of a driver subjected to an applied musical signal we must look at the forced response of the driver, not the "natural" or unforced response. The natural response does affect the forced response but the natural response comes into play mainly if the signal is abruptly stopped at a time what the driver's moving structure is not at its rest position or, if at the rest position, when the moving parts still have some velocity. However, for music unless we abruptly turn off the signal, the natural decay of a musical instrument or even our voices is generally much longer than the decay of a driver from some non equilibrium position.

Several years ago Linkwitz and I were involved in a discussion about "fast bass" and the role of damping on how a woofer sounded. At that time we agreed that the difference is the sound of a sealed box woofer with Q = 1 and Q = 0.5 has more to do with the characteristic of the amplitude response than the damping. In fact, it can easily be argued that a Q = 1 system is over all more accurate that a Q = 0.5. This is because above the system cut off frequency the Q = 1 system has generally more uniform amplitude response and flatter phase. But the point here would be that in just about any musical reproduction system we are going to be dealing with Q's typically 1 or less. As an example consider a woofer with a 32 Hz cutoff playing low C (also about 32 Hz). On a Q = 0.5 system that note's fundamental will be reproduce at a level 6dB below the input level but the harmonics at 64 and 128 Hz be reproduced at pretty much the correct levels. The Q = 1 woofer will reproduce the note with the fundamental at the correct 0dB level and in correct relation to the harmonics. Yes, if the note were abruptly stopped the Q = 1 system would take a cycle or two longer to reach an inaudible level, but when it is considered how many cycles it takes to first recognize that the tone is in fact low C this is generally insignificant.

The point is that music does not (unless electronic) behave like a signal generator being switched on and off. And, even if it did, the consequences are insignificant as long as the frequencies contained in the signal are well above the low frequency cut off of the driver. That is because above resonance a driver does not behave like a mass on a spring. It behaves as a mass driven by a force over most of its useful operating range. When the equation of motion for the driver is written it is observed that the contribution to motion by the spring force decreases as frequency rises as 1/(f/fo)^2 and the damping force contribution decreases as 1/(f/fo). At resonance all 3 components, mass, spring and damping play equal roles. Below resonance the mass contribution decreases a (f/fo)^2 and the damping contribution as f/fo.

[sreten]

Originally Posted by Overkill Audio

Thanks in advance
Derek.

Hi,

No thanks. Your document is so wrong in so many respects its not
inviting any sensible discussion of anything related to bass drivers.

Its pseudo-technical drivel of the form those that don't understand
what is actually going on love debating, whilst still having no real
idea what is going on, and technical details only get it the way.

So there is utterly no point trying to illustrate the reality, deaf ears.

rgds, sreten.

(1) is irrelevant given the described scope of the "paper". The
idea that 99% of audio types actually understand it is beyond me.

[Overkill Audio]

Hi All,

Thanks so much for all your feedback, lots of ideas, most of which I had not thought about before…!
A few initial thoughts in order of questions are:
PbAg, Good point! It adds another force into my “Ping pong ball model”.
A few points / questions spring to mind.
(1) As typical HiFi drivers are usually under 1% ( often as low as 0.3%) efficient and top Pro drivers still only 2% to 4% ( Horns / CD drivers can be 10% plus) where does the 9.8 watts of our 10 watts input ( or 98 watts out of 100 watts etc.) go? Are you saying it stays in the “system” ie in limbo or in a perfectly balanced force meets opposing force scenario in between the amp output and the driver cone / voice coil? As we are constantly pouring in more and more power there must be an “ outlet “…. Heating of the voice coil is one well documented way to dissipate energy. My doc suggests that driver oscillation dissipates a lot more...!
Your taping cone with and without amp connected test is interesting… it uses kinetic energy ( the physical tapping) as the input and the amp as an electrical brake… so where does 98% plus of the energy go…?

Dave, lots of interesting ideas, may I please question your idea that:
“Another interesting point is that the system only looks like a mass on a spring in the vicinity of resonance.”
I just don’t get that at all! Not only don’t I understand your point but in audio we only use drivers above resonance 95% of the time…!
However your key point I feel I must still ( sorry!) disagree with is “the motor does not turn off when the signal stops. “
My thoughts on this are:
When you break down natural sounds ( i.e. not electrically generated Sine waves / square waves etc.) they are just a compression / rarefaction of the air followed by a decay back to ambient pressure. This is the only way our ear brain mechanism can hear anything from a single snapping twig to a full blown orchestra. So if we ask an amplifier and speaker driver system to reproduce a single snapping twig we now need to factor into my ping pong ball model the amplifier “damping”….My question remains where does 98% of the electrical input from the amp go? How is it dissipated or stored?
Two vital points to bear in mind is that all music / vocals are just a series of “ snapping twig “ compression / rarefaction air pressure changes & decays… Regardless of how many sonic events (snapping twigs) are happening simultaneously, or what SPL or frequency they are or whether it is a drum / hammer strike, a bowed string of vibrating vocal cord its all made up of individual sonic events that have two key parts, an ultra-fast rise time ( the compression or rarefaction) and a much slower decay back to ambient air pressure.
Quite mind blowing when you actually look at how complex it is to just sit back and listen to an orchestra!
So when the amp sends the electrical pulse of a snapping twig / piano note or whatever to the driver, it is a ultra-fast rise time with a much slower decay …The total length of time from start of rise time to end of decay is FINITE! It may vary from very short to quite long ( relatively speaking) but it is finite. An individual event. The fact that there are 100, 1,000 or 100,000 other sonic events happening in close succession and or simultaneously cannot change the basic composition of sound OR the way our ear / brain detects it…!!
Hi Conrad,
Yes I think it all comes down to energy storage / dissipation.
We are pumping in electrical energy in a constant flow that never switches off, in order to simulate a discreet series of sonic events.
98% or more of the energy is wasted as a combination of heat ( voice coil) or as friction / heat ( cone / spider/surround oscillation)…
John,
Thanks John there is soooo much in your post I think I need more time to do you justice! I will ponder and reply tomorrow.
In the meantime do any of my points above impact your thoughts on the subject?

Thanks again to all of you.

Cheers
Derek.

[AllenB]

Originally Posted by Overkill Audio

“the motor does not turn off when the signal stops. “

Think of the amp as holding the speakers hand like a child. Wherever you go, the child will follow. They will not always follow you precisely but in the end you'll reach the same destination.

individual sonic events that have two key parts, an ultra-fast rise time (the compression or rarefaction) and a much slower decay back to ambient air pressure.

Why must the decay be slower than the rise? Rooms and instruments may produce a decaying sound but this is different.