posted 08 March 2002 01:07            

But, aside from that, I recalled last night that reflection from hard surfaces causes a phase inversion. My friend and I have been arguing all day long about this. I trust the wave equations, but he has more experience with speaker systems than I do. So to convince him, and to double check the result for myself, I put Kyma to use this evening here in the lab... It is a really simple minded experiement and trivial for Kyma...

I turned one of my speaker systems to face the wall of the lab, about 15 inches from the wall. About midway between I placed my Earthworks omni so that it would pick up the direct wave from the speaker as well as the reflected wave from the wall. Then I had Kyma produce a slowly swept sinewave running logarithmically from 40 nn to around 108 nn (about 100 Hz to 4 KHz) over a period of 1 minute. Piece of cake with Kyma!

I recorded the mic channel along with the drive signal in the left and right channels of a stereo track. The drive signal was carried as a check on the mic channel. Using a spectrogram display, tuned in intensity levels to show good contrast between minima and maxima, I spotted a good set of 6 consecutive minima. Their mean frequency difference was about 445 Hz +/- 32 Hz, which provided a measure of the local speed of sound to be around 1200 ft/sec. Still within 10%.

Then I set out to determine from the acoustic interferometry equations what and whether there was any excess phase shift coming from these measurements. My friend insists that it can't be so. He is incredulous to my claims. But sure enough, with blinders on, just crank the equations and do a least squares fit to the data and you find that there is indeed a phase shift of half a wavelength at all frequencies on reflection from a wall.

This result is consistent with the physics of organ pipes closed at one end. You all know about that stuff, having used Kyma delay lines to create your own resonators...

So the equations don't lie. There really is a phase reversal on sound reflections from large hard surfaces (i.e., walls).

Now, I'm no audio expert, and I have heard a lot of the pros talk about room corners being "bass traps". I have always wondered what that really means. I think now I understand. If you have a speaker radiating equally in all directions, then a speaker mounted near a corner will have severe phase cancellation due to the back reflections, especially at low frequencies where the distance to the wall is a small fraction of a wavelength.

But maybe I'm all wet about this new understanding. Any of you audio pros out there care to correct me on this? I am eager to hear your opinions!

posted 08 March 2002 07:01            

Anyway

When I think about sound in air I have to keep reminding myself that it is energy and as such cannot simply be a simple single sine wave. As energy cannot be produced from nothing and cannot disappear to nothing ,then the zero points of a sine wave break the laws of physics. Instead a sinewave in air contains kinetic energy as the air is moving and potential energy when the air is under pressure.These two energies are 90 deg out of phase with each other such that the sum of the square of these, form DC or constant energy.
Now when the sound hits a wall, the air has its direction changed and therefore creates an antiphase signal but a high pressure will remain a high pressure and the phase of the pressure wave will not be reversed. So its important to know if your mic is acting as a high speed barometer or a high speed wind detector. I suspect its a bit of each. I wonder if different mics would give different results.

How about testing the mic and speaker without the wall and using that as a reference to compair with the wall version.

I seem to have just come up with more questions.

I hope I haven't missed the point.

regards

Pete.

posted 08 March 2002 12:52            

Well, as for detecting a "sound wind" these mics would have to be able to detect molecular motions that are on the order of the size of a single atom or smaller... And even at the loudest sounds the ear can tolerate, far louder than I used last night, the maximum displacement will only be on the order of 10 microns or so.

So it is rather unlikely that my omni is detecting much of this direct kinetic energy. However, there are a class of transduscers, known as hot-wires, that are capable of detecting air flow to very low values. I don't know if they could be used as "microphone" detectors of not. I have heard of people using these sensors inside of wind-tunnels. The air flowing past these hot wires cools them by minute amounts, changing their resistance a smidge.

I fully expected the results I got last night. Recall the way a closed organ pipe works. These form quarter wave resonators, which is only possible because of the phase reversal at the closed end. An open tube is a half-wave resonator, and so its resonant frequency for the same tube length is twice as high as that for the closed tube.

The wall in my lab represents the same kind of barrier to sound as the closed end of a large organ pipe. Hence it should behave similarly on sound reflections from this "closed end".

But it is interesting that you mention the large tubes placed behind the sofa. Those must be acting as comb filters, much like our Kyma delay lines with feedback.

Your point about conservation of energy is well taken too. But the absorption of sound at the walls, which give the reflections their spectral coloring, helps to dissipate that sound energy by converting it into minute amounts of heat. If they didn't imagine the resulting chaos in your studio that would accumulate for all the sounds made during the course of a day.

My room-effects calculations showed me, for a trial run with image sources held in the room plane out to 200 feet, that the maximum number of reflections at this delay time (about 0.2 sec) was 15 or 16. The distance of 200 feet already drops the signal by 46 dB due to the 1/R^2 effect. If my room here cuts off its reverb tail after these 200 ms, then it means that my walls must have absorbed another 14 dB from all these reflections, to get to the -60 dB cutoff point. That means my walls must be absorbing about 1 dB on each reflection, which seems, to my mind, totally reasonable. (Not much of a recording studio here, is it?)

Cheers,

posted 08 March 2002 22:41            

But that chapter does point out that the use of absorbing patches on the walls is most effective when placed randomly, instead of in a regular pattern. He also points out that absorbing material placed in room corners is twice as effective as when placed elsewhere.

In general these patches are used only for controlling reverberation times of various normal modes in the room. They need to be placed along the wall where the pressure is highest for the troublesome frequencies. Absorption is highest where pressure is highest.

The room shape and dimensions are most important for determining which frequencies can be faithfully transmitted throughout the room. He points out that you need 10 or more normal modes in a frequency range dF that is proportional to the inverse characteristic time of a pulse that you wish to transmit. An example for a room measuring 10 by 15 by 30 feet, and a pulse lasting 1/10th second (dF = 10 Hz) can't transmit that pulse very well below 150 Hz. This has nothing to do with the absorbing material on the walls, but instead is a result of the low number density of normal modes in the room below 150 Hz.

A large auditorium on the other hand only gets into trouble below 10 Hz or so. So the important audio frequencies manage to transmit just fine.

So apparently, my concern over phase reversal on wall reflections is important only for experiments like the one I ran to measure the speed of sound in the room -- Audio Interferometry. Outside of that, it has little practical use...

posted 14 March 2002 08:46            

When I'm asked to explain how sound works (which in my job is quite a regular thing), I've always given this explanation, but I'm going to have to stop destributing this false knowledge.

When a speaker generates something like a 100 hz sinewave, the speaker cone moves back and forth 100 times a second by about 1 mm. The air that is touching the surface is being pushed and pulled at the same rate. This makes a tiny puff of wind that lasts for 5 msecs followed by another puff of wind in the opposite direction for 5 msecs. The air that is a little bit away from the cone doesn't move imediaitly due to the elasticity of air, and the fact that air has mass and is subject to momentum. The air gets squashed. That squashed air then trys expand back to the norm and in doing so pushes the next bit of air away from the speaker.The next half cycle the air moves in the oposite direction and the air is stretched. The leading edge of this activity makes a similar activity in the next chunk of air. This is how sound can move large distances in one direction but the deviation of the air from the norm can be small. But if the air doesn't deviate or move by any more than +/- one atoms width, I don't understand how the air pressure can change at all. I thought air pressure was the dencity of air molicules and therefore to change the dencity at any point in space ,air molicules would have to move in or out of that space. Have I missunderstood what air pressure is?
I always thought that a moving coil mic worked by alowing a diaframe to move backwards and forwards freely with the air around it such that the velocity of the air would cause a coil to generate electricity and would give an air velocity wave form(a high speed wind detector). and that a crystal mic had a ridged surface that would not move much at all but would sence the change in air presure(a high speed baromiter).

When I spoke about a DC energy signal I should have called it a decaying arc of energy as the energy gets desperced as heat but I thought that was obvious. My point here was that, at no moment in time does the energy level go upwards as it would 100 times a second if it were a 100 hz single sine or cos wave.
Which leads to my next missunderstanding.
I thought that the loss of energy to heat was caused by friction of moving objects . Pressure can be kept in a jar for years and not loose any energy, so if the air movement is so small(less than one atoms width) what generates the heat and inturn the loss.

posted 14 March 2002 12:28            

It is a confusing topic, and lots of misunderstanding abounds. You and I are accustomed to walking outside and feeling the wind in our face. That really is a flow of air molecules past us, and it would seem natural to assume that sound causes such mass motion too. But let's try to examine some common misconceptions and come up with some good answers.

Pressure is a force per unit area, not a measure of energy per se. If you want to discuss energy, or power, of sound, then you need to multiply sound pressure variations by the velocity of the pressure wave. That is a measure of power flux or power transmitted per unit area in some direction. A bottle full of compressed air has a lot of pressure, but no velocity, and hence only has the potential to produce power flow when later opened.

Microphones can't directly measure this power flux. They respond instead to a kind of average of pressure variations with time over the area of their diaphram.

The air in a room where no convection wind exists, looks at a microscopic level like a soup of molecules of oxygen and nitrogen mostly. These molecules are almost snug up against each other. There is a common understanding that at normal temperatures and pressures, 6.02 times 1 with 23 zeros after it, as a number of molecules, takes up 22.4 litres of space. If you work out what that means per molecule then you find that each molecule is no more than about 3 nm (billionths of a metre) from one another. That's roughly 3 or 4 air molecules width apart from each other.

So in other words, once set into motion, an air molecule can only travel about 3 or 4 diameters before it knocks into another molecule. But these molecules are all roughly the same mass, 32 mass units for the oxygen, and 28 mass units for the nitrogen...

Think of a billiard table. What happens when the cue ball strikes another? Depending on the angle of contact, it either gets diverted, imparting some of its original momentum to the other ball, or on a direct strike, the cue ball comes to a halt and the other billiard ball carries onward. This same behavior happens with the air molecules.

So as these air molecules are bouncing about they keep knocking into one another and on average they don't go very far from their starting position.

Now enter a sound wave, say 1 KHz, at some modest loudness level. That loudness level tells us something about the pressure, or density change, in the wave as it propagates past our microphone. But the sound wave is itself, not a grand motion of air molecules, but rather just a tendency for many molecules at once to be moving in a common direction, slamming into other molecules and then coming to a halt, while those molecules just slammed into take up the motion for themselves. And the cycle repeats, all just for one leading pressure crest from the 1 KHz sound. Viewed from a distance this creates a sort of bunching of molecules in an advancing density wave, leaving regions of slightly lower average density in its wake.

But our sound source, the speaker, keeps vibrating and starting new density waves in the room air with every cycle of the 1 KHz sound. Overall, even after several minutes of this, the room is filled with the sound, but any given air molecule has barely nudged away from its starting position. The sound message is relayed by means of a chain of billiard balls each relaying its momentum message to the next, and passing the message on down the line to the next molecule. Like a big bucket brigade.

Now you aren't entirely wrong to view the cone of the speaker as creating a small wind, and very near to the cone you could measure convective motion of air. But that dies out quickly due to this molecular knocking about. That molecular knocking about is the conversion of motion into heat, which is nothing more than microscopic motion of molecules.

So terms like pressure and density really only apply when viewing the system from afar, averaging the behavior of molecules over grand ensembles. At a microscopic molecular scale there is no pressure, and no density. Just little billiard balls smashing into one another repeatedly.

Or so goes our highly successful mythology about how nature behaves... I used to caution my students that these are merely our mental pictures for how nature behaves, but don't mistake them for the real thing. Nature does what it does, whether we understand correctly or not. Our confidence in our mental models is bolstered only over time and with being able to make successful predictions based on them. But one sour result and we are obliged to discard the model and begin anew.

I'm sure I haven't answered all your questions here, not that I even could... But I hope this helps. If not, ask away and we'll try some more!

Cheers!

- DM

[ Here's another example of a density wave -- I used to study these extensively while trying to answer why galaxies form spiral arms --

This one, unlike the sound waves, actually is a mass flow on average, but the wave is a sort of illusion. Imagine riding in a traffic observation helicopter high above the traffic of a large city or a busy highway with periodic stoplights at road intersections. Looking down at the traffic you will notice regions of bunching of cars near stoplights, followed by regions of lower density where the cars spread out as they move past the intersections. What you are seeing is a density wave. If you blur your vision and try to see only this density variation and not individual cars, that density wave might even look like it is moving backwards over traffic sometimes, and at other times it might be moving in the same direction. But regardless, it probably never moves at the same velocity as the constituent particles (automobiles in this case). The "density wave" has a life of its own. In this case, it doesn't carry energy and can't be used to transmit a message, but it is a wave nonetheless.

We used to envision galaxies with spiral arms as a byproduct of competing or interfering spiral density waves. One wave propagates outward from the center of the galaxy, while the other wave propagates inward. When these two competing spiral density waves interfere constructively, as with sound, the appearance of a spiral arm emerges.

The wave particles -- gas, dust, stars -- all actually move in more or less circular orbits about the center of the galaxy. They don't permanently reside on those spiral arms. They actually move through the arms, bunching up at the leading edge of the arms as they pass through. The spiral arm pattern can even appear to be moving opposite to the motion of the individual stars. So once again, the density wave is an illusion. ]

posted 14 March 2002 13:13            

"Microphones can't directly measure this power flux. They respond instead to a kind of average of pressure variations with time over the area of their diaphram."
It seems that most microphones measure the pressure or potential energy by converting into movement or kinetic energy. In your example, wouldn't the billiard balls knock into the mic diaphram, causing it to move? From the amount of the displacement we could infer the amount of pressure that caused it. This measurement would then have to be "transduced" back into a voltage (i.e. "electrical pressure") wave in a condensor mic or into a current (electron flow?) for a dynamic mic.

It makes me curious whether there is any way to measure pressure directly without converting it into displacement. Even a classic barometer measures changes in DC pressures by a change in the position of fluid in a tube.

BTW, Lippold Haken (Kyma-ite and Continuum designer) has done some interesting measurements on the aerodynamics of speech production by measuring air flow very close to the mouth. He was able to replicate the classic studies of Taeger and Taeger. (Like the speaker cone, the air flow is important only in the immediate vicinity of the source, after which the signal is transmitted by acoustic waves, but it showed that some of that signal is due to vortices and turbulence in the mouth, not exclusively due to glottal pulses). Hot wire anonometers are very expensive instruments, so Lippold made his own hot-wire mics by breaking off the top of an ordinary light bulb and using a Wien Bridge circuit to measure how the resistance of the filament was changing with temperature. ;-)

posted 14 March 2002 13:19            

I propose that we try to spell out the word "Kyma" using traffic density waves. I will connect the output of the Capybara to control the traffic lights, and we can all go up in a helicopter to read the message as it is inscribed on the highways below us! Rather appropriate, since kyma means "wave" in Greek.

posted 14 March 2002 13:25            

Lippold's technique for making hotwire anerometers sounds very intruguing! I'm not surprised by the importance of turbulence in speech. Turbulence is also very important for the production of sound in organ pipes, flutes, and reed instruments. But as you say, these effects die out within a short distance from the source.

The pressure and velocity waves are both related to energy, but they aren't energy themselves. The power flow in a sound wave is measured as the product of pressure and velocity. That's the important factor for sound absorption by wall panels and baffles. Pressure alone, and velocity alone are not the directly important quantities.

The air molecules do knock into the microphone diaphram causing a minute displacement on average when the "pressure" is above ambient, and conversely. But in a condenser microphone you are really measuring the change in capacitance of a thin foil diaphram acting as one plate of a capacitor. It isn't the velocity of the diaphram per se, but the actual displacement. However, without motion to and fro, you only get DC offsets and no audio. So in that sense the velocity of the diaphram is important for conveying audio information.

I would imagine that one can make a pressure transducer out of stress or strain measurements. But even in that case we must have a minute displacement in order to create a stress or strain. But this displacement is probably orders of magnitude smaller than the displacement of a microphone diaphram.

posted 15 March 2002 08:42            

I looked at your billiard ball example and can see the floors. First if we look at what happens when one moving ball hits a static one strieght on (as you mentioned) then the moving ball will stop dead but the other will move at the same speed as the first (less the losses) in the same direction. Therfore the signal would get transfered at the speed that the original que moved(plus a bit to take into account the ball width and gap between balls) and would slow do as the signal died away.This would mean that the speed of sound would vary dependant on the amplitude of the signal, which of cause it doesn't.
Also the air either side of the speaker would be swepted away after first cycle and we would then get silence as there is nothing to push the balls back.

But if we make a minor adjustment to the model it becomes a whole different story.

If we lay out the balls evenly in a matrix grid across the whole billiard table and put springs between each ball and its direct neighbours, and then we squashed them all together so that they where pushing out agenst the cushons of the billiard table (we'll call this force 22 lbs/in2 just for fun), then we have a new model that has very diferent properties. Now if you take your cue and hit one ball in the middle of the table it will form a shockwave of ball movement that will move out towards the outside of the table at a fixed speed regardless of the speed you hit the first ball. Also all the balls will settle back to there original position eventually.
An important point here is that the balls could easaly move from there original position by more than ten inches while the distance between any pair of adjacent balls need never have changed by more than a fraction of an inch (asuming the table is big enough). Could this fraction of an inch be the equivelent of the "less than one atoms width" that you were talking about and that the molicules realy can move much farther.
Please say yes as it will all make sence again.

Another point here is that the balls can move at different speeds but the waves always moves at the same speed.

At any one moment in time we could freeze the state and messure the kinetic energy of any balls that are moving and also, for any springs that are more squashed than they were at the start, calculate the energy required to squash them that extra bit, less the reverse for the springs that are stretched more than the norm, then apart from the friction losses we could add them all up and get the same energy as that that the cue passed to the first ball it struck.

This is more like the picture I had in my head at the beginning.

With regard to mics, if we look at a moving coil mic, this has no phantom power sent to it and no battery. It normaly feeds directly into a 600 ohm resistor on the input of amplifier. It can easaly produce a voltage across that resistor with of peaks of up to 1 mV at normal sound level. The amplifier supplies no power to this input it simply reads the voltage across that resistor.Therefore at that peak moment in time the mic is generating 1.66 nano Watts and this power has come totaly from the sound in the air, as there is no other power source around. It may be small but it is real energy.

posted 15 March 2002 12:13            

In a water analogy, wind is like current. If you stand at one point and you have really, really, really good eyes (or a suitable scientific instrument), you would see water molecules travel past you. The water is actually moving.

And sound is analogous to water waves. The water doesn't actually go anywhere, only the wave does. If you stand at one point, you would see the wave disturbance travel past you but the water molecules only move back-and-forth.

Likewise with sound. Wind is air in motion. Sound is air vibrating.

When I think of sound traveling through air, I imagine air as tiny distributed masses which are elastically coupled together. Here's my mental picture - Take a ball-bearing and attach small coil springs to the front, back, left, right, top and bottom. Think of the ball-bearing at the center of a cube and each spring extends to the center of a cube face. Make up a bunch of these (try to get your kids to help). Now glue them together so that the end of one spring is attached to the end of another, as if you were stacking cubes. You will end up with a cube of cubes.

Now if you stuck one of the ball-bearings with a sharp percussive blow, the disturbance will propagate through-out the structure as a wavefront. As the struck ball-bearing moves out of place, then bounces back-and-forth, it disturbs it's nearest neightbors, which causes the whole neighborhood to get disturbed. (While this is like a college campus on a Saturday night, it's also reminiscent of a sound wave.) You would see a compression wave followed by rarefraction, followed by a lesser compression, followed by a lesser rarefraction, etc. The wavefront would be 3 dimensional and spherical. Eventually, the disturbance decays. In the meantime, the temperature of the springs has increased slightly due to friction. Likewise, the temperature of the air increases due to the sound wave causing the air molecules to rub together.

Say that you measured the instantaneous air pressure at a point while a sound wave pass by. Say that it is a sine wave. Before the wavefront reached you, you would measure some nominal air pressure. Call it the zero point. As the wavefront hit you, you would see the air pressure rise smoothly along a sine curve. The compression part of the wave is the positive part of the sine wave. It rises to a peak and starts to decline. As the wavefront proceeds through the rarefraction portion, the instantaneous air pressure drops below the nominal pressure, i.e., below the zero point. The rarefraction corresponds to the negative portion of the sine curve. As further parts of the wavefront pass by you (further compression/rarefractions), you would trace-out a decaying sinewave.

In our ball-bearing analogy, air pressure corresponds to the distance between the bearings. Higher pressure equals smaller distance.

Watch what happens when the wavefront hits a wall. Assume the wall is perfectly rigid. As the compression hits the wall, the natural tendency is for it to rebound. Unfortunately, there is more compression wave behind it (remember, we're still sliding up the sine wave). No place to go. The wavefront is trapped. The pressure builds. But wait! Now the rarefraction hit the wall. Ah! Now the rebounding compression wave can expand into the incoming rarefraction! Likewise with the successive compression/rarefractions. Result? The reflected wave is out of phase with the original.

With the principle of superposition, we can generalize this result to non-sine waves.

posted 15 March 2002 12:49            

I think part of the problem of visualization comes from the fact that there are sooo many molecules available in just a small volume. Imagine, in 1 litre of air space, there are approximately 26,880,000,000,000,000,000,000 molecules of air. With all these guys jostling about and smacking into one another, you find that on ensemble averages the speed of sound is constant in air, just like in a crystaline solid, and that the speed of sound is not dependent on frequency -- at low enough frequencies.

But Dennis has the right idea, and so does Pete, about the nature of the wave propagation. It can propagate freely while hardly moving any of the air molecules at all. Like the water wave, it progresses, while the medium just moves slightly to and fro.

posted 07 April 2002 10:19            

Well actualy we can.

If we take a sealed room and devide it up into cubic inches then we know that air like water finds its own level.

So therefore although molicules are traveling freely between adjacent cubes we can say that at any one time the number of molicules in any one cube will almost the same as in any other cube on the same horizontal plan. Of cause the cubes at the top of the room will have slightly less molicules but not much.

Now what about this totaly random velocity of air molicules ?

Well if one air molicule moved from left to right at a velocity of 2 inches per second, then another molicule must travel at 2 inches per second to the left OR 2 molicules must travel 1 inch per second to the left OR 4 molicules must travel 1/2 inches per second etc to compencate. This has to be true to maintain equilibrium.
It doesn't take much thinking about before you realize that for any choosen aria the velocity of all the molicules in that aria added together is ZERO.
Now if we cause a momentary high pressure zone by moving something in the room we can see that for an aria to have aquired more than its fair share of molicules, there must have been a moment before hand where the total molicule velocity of one or more of its neighbouring arias, must have amounted to something other than ZERO and in the direction towards the high pressure aria. (It must have got its extra molicules from somewhere).
So our balls and springs moddel can be as representative of the movement in air as it would a solid like crystal. I know that this doesn't take into acount that different molicules have different masses But the rules that govern Pressure differance, average velocity ,mass, kinetic energy and potential energy still work, without having to study every single molicule independantly.

posted 07 April 2002 13:20            

You've got a pretty good intuitive understanding of how things work. And you are correct that we can't compute on every individual molecule of air.

Instead, we use something called "Statistical Mechanics" to describe the behavior of large aggregates of molecules. But these molecules are not bound as tightly as your ball and springs model would indicate. As I mentioned before, that kind of model is more suited to crystalline structures. Air is a much more loose collection of molecules, and they only interact when they are nearly in contact with one another -- which happens quite often mind you.

Let's see, at room temperature, these molecules will be knocking into each other at speeds of a few hundred meters per second -- very close to the speed of sound. But they can only move about 5 molecule diameters before they knock into another molecule.

But you have some good thinking based on your reasoning about equilibrium conditions. On balance, there cannot be any large difference in the numbers of molecules moving in some direction compared to those moving oppositely.

The ball and spring model simply couples these molecules too tightly to one another and causes them to be interacting at too large a distance from each other. The model using elastic collisions more closely resembles the conditions at normal pressures, densities, and temperatures. At much higher pressures, densities and temperatures, the inelastic qualities must be taken into account as energy is repartitioned into vibrational and rotational modes, but at normal conditions these are not very important.

posted 08 April 2002 12:09            

In the ball and spring model, each ball is supposed to represent the accumilated mass and velocity for one cubic inch of air and the springs are to represent the pressure in one cubic inch of air. Not each molicule.

posted 08 April 2002 14:51            

I'll have to go back to the drawing board.

posted 08 April 2002 16:24            

You're on the right track here. It's just that a ball and spring model couples the masses too closely to one another for a gas model. But most of the interactions at standard temperature and pressure will be elastic collisions as you were reasoning. It is the collision transfer of energy that accounts for the propagation of sound. So you don't need much in the way of mass flow to accomplish that. There really isn't a need for a "sound wind" per se.

Also a ball and spring model would imply a build-up of potential energy as the molecules displace from their equilibrium positions. On average then you would expect to find a sizeable amount of energy stored up in any cubic volume of air. That just isn't seen. There is a storage of energy in diatomic molecules -- notably the rotational and vibrational modes, but these get released as temperature is lowered in a manner that is quite different from what you would find with a spring bed storage of energy.