audio qualia 2

what if we play with parameters

with calculations, it's possible to play 'what if'. Here, certain parameters are altered to illustrate the affect of changing one at a time. First off, the thickness of a plywood panel, easy to do in practice, but the usual thing most people assume is the 'thicker the better', arguing that mass in increasing. It is, of course, but is that a good thing? Watch the video to see the sound loss decrease with increasing thickness/mass, along with critical frequency and dilatation frequency. Not what we want!

 

 

The optimum thickness is 11mm for a panel of this size, made of Baltic ply. But the general sound loss is only around  15 - 25 dB, with a dip down to just 7dB loss at the fundamental resonance frequency (about 150 Hz) and down to zero loss at the critical frequency (2880 Hz), where the whole panel is transparent to sound (around that frequency). The goodness factor, estimated by integrating under the graph, from 20 Hz to 1kHz, for 11mm plywood is 1425. 

 

 

 

 

 

 

 

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What if we could increase the density of the plywood? With this modeling, it is possible to play 'what if?'

 

 

We can see that by increasing just the density of the plywood from 650 to 1420 kg/m³, if that were possible, more sound loss is possible. The goodness factor increases to 2021, not bad.You can also see that the fundamental resonance frequency has decreased in value (to about 80 Hz) and the critical frequency has increased to over 5 kHz, but, the overall loss is much greater with increase in density. 

 

 

 

 

 

 

 

 

Now what about increasing the plywood's stiffness, (Young's modulus), increased to 10 GPa from 7.5 GPa?

 

 

 

The result is a little disappointing, the goodness factor has gone down a little, to 1332, the fundamental resonance frequency has gone up, and the critical frequency has come down, so stiffer panels are not better in this instance

 

 

 

 

Now, changing the Poisson ratio, from 0.28 to 0.4, produces not much change at all, goodness factor was 1397, nearly the same.

 

 

 

 

 

 

 

 

 

 

 

 

And lastly, what if the damping factor is changed, to 0.75?

That looks a bit better, with a goodness factor of 1850, but still big dips at about 150 Hz and 2500 Hz.


 

 

 

 

 

 

 

 

However, if we change all the previous parameters at once, we get:

 

 

 

 

 

that looks a lot better, with losses greater than -20dB right across the spectrum, a minimum value to aim for, perhaps. There are two interesting things about this result. First of all, the goodness factor is 2303; if we add all the individual parameters together, that is the differences from the original 1425, we get 2325, virtually the same number. Is this coincidence or does it suggest the individual parameters are independent of each other?

 

 

However, the changed parameter values were not chosen at random, they are, in fact, those of Panzerholz, a type of superply, made from wood veneer and resin. The optimum thickness is around 24mm, and looks like  this:

 

 

 

 

The optimum thickness gives a goodness value of 2842, an excellent figure, and provides losses of about 40dB or more nearly right across the spectrum, but by increasing thickness, the fundamental frequency has increased and the critical frequency decreased, but we have achieved a much smoother loss curve with broad resonance peaks.

 

 

 

 

 

This graph is typical of a material that is suitable for plinth duties. The quite sharp dip is the critical frequency region. Above this frequency loss is about 12dB/octave, and controlled by the damping factor. The other major dip, around 300Hz, is the fundamental frequency, the peakiness of which is controlled by the damping factor. Between the fundamental frequency and the critical frequency is a region of loss, increasing at about 6dB/octave, and controlled by the mass of the plinth. Below the fundamental frequency is a region controlled by the stiffness of the material, loss is about 3dB/octave. As here:

 

 So, how does a panel of a material, which could be used for plinth duty, actually do its job, that is, reduce the amplitude of the vibrations fed to it by the deck, as well as aerial and possibly seismic intrusions? To understand that, we must understand how it vibrates.

Imagine a rectangular panel, say made of wood of some kind, supported at its four corners.  If we press down in the middle of it, a slight flexture will result. If we take our hand away, it will return to its original position. In this case, the panel will move as one, and is how the panel moves in the stiffness region. The flexure starts on the side we depress, and continues through the panel until the other side is reached, then the process is reversed. As the flexure wave passes through the panel, and if the material is composed of microscopic (or large) particles, the particles will move relative to one another, and friction can result. The friction causes heat, so that the original flexural energy is converted into heat energy, although some of the original energy can also be re-radiated as sound waves.

Note that we are talking about panels that bend, and that the sound waves are not thought of as light rays, as is often the case. This is about bending and friction. In the case of a plinth and a turntable, the mechanics of the turntable can produce vibrations, and when efficiently connected to a panel (called coupling), then the turntable and the panel bend as one. And the friction reduces the amplitude of the vibrations, as heat. The more friction, the more damping. And as damping is the exponential loss of vibrational amplitude, over time, any material with a high intrinsic damping factor value will damp a vibration faster that one of lower damping factor value.

 to be continued...............