Hello Steve,
I know I better should find some more time to explain all different phenomena in detail on a page with graphs.
Lets first speak about the strongest phenomena of double leave systems:
1) MASS-SPRING-MASS RESONANCE
Basically the main calculation starts from the Mass-Spring-Mass resonance, let's call it further fo.
This is the most powerfull source defining the acoustic behavior.
Theoretically at straight incidence:
Assume a complete undamped theoretical system:
fo = insulation 0 dB. In practice there is damping by the connection structure edge clamping and whatever. So fo is not 0 dB but its the lowest point.
From there the TL rizes theoretically with 18 dB per octave in practice with 12 dB per octave.
Starting point of this inclining line is "fo" at the level of the mass-law of both leaves together.
So it's clear the lower this point the better since it also influences the subsequent higher frequencies, in fact you shift this inclining straight line to the left.
Improving a double leave wall is mainly trying to get this "fo" as low as possible. Al the rest is secundary.
This is defined by the combination of the 2 masses (both wall leaves) versus the stifness of the spring.
You increase insulation by:
a) increasing the masses (more layers)
b) weakening the spring (increasing cavity width)
Note that I don't speak about waves here: the cavity is much too small to ellow those long low frequency waves to develop.
The cavity acts as a pressure room, which is about comparable with sound in a room far below the lowest room modes. That's why wavelengths do not matter here the air is only a spring.
Here you see something fun:
A drywall = exactly equal to a panel bass trap.
Just flip the TL graph upside-down, substitute the TL values by absorption values and see, there you are.
The Q of this dip depends on weight versus spring ratios damping and so on.
This inclination of 12 dB/octave changes in 6 dB/octave when point 2 starts:
2) THE CAVITY RESONANCES
Exact as in a room there are cavity resonances or modes, where the first cavity resonance is located at 1/2 wavelength.
However the width of this effect causes this downward bend from 12 to 6 dB per octave to start earlier at 1/4 wavelength or even below.
Then we come to the 3th phenomena:
3) THE COINCIDENCE FREQUENCY in US called CRITICAL FREQUENCY.
This is where this previous described rize of 6 dB/oct bends down the a decline of the curve towards the coincidence frequency.
Here I copy another message including the link you know:
Look at:
http://www.domesticsoundproofing.co.uk/tloss.htm
If you want the math I suggest to get a book in the library about
acoustics.
The coincidence freq., in the states more referred to as the critical
frequency.
This is the frequency where the wavelength of the incident soundwaves
equal the bendingwaves in the panel itself.
This causes a serious transmission loss dip.
Some general things:
Doubling the thickness of a panel will lower this frequency with 1
octave.
It depends on material properties. E.g. this frequency positioning is
better for drywall than for wood, making drywall better for TL.
This frequency is angle of incidence dependent.
It is about the only frequency where the radiated noise on the
receiver side preserves the direction of the incident noise at the
source side.
Below this frequency the bending waves in the panel become shorter
than the wavelength of the incident energy.
This causes the radiation ratio of the panel to become lower than
100%.
What happens is that the air pressure toggles between the crests and
the throughs of the bending waves of the panel. As such only part of
the vibration energy is transformed in noise again.
In fact one could interpret this a bit as natural anti-noise (poetic
licence).
That's why things as drywall are such efficient insulators.
Above this frequency the bending waves in the panel become larger
than the wave length of the incident energy.
This causes the radiation ratio to become 100%. Every bit of
vibration is converted again to noise at the receiver side. The wall
act a bit as a piston.
In my language (literally translation) we call a wall with very low
coincidence a bending-stiff wall (as e.g. a concrete or brique wall),
while a wall with very high coincidence we call a bending-soft wall
(as steel plate, drywall, particle board etc.). In US one refers to
the latter as a flexible wall or panel.
Best regards
Eric
Now: If you once should find the time to play with the excel files on my site you REALLY should get more the feel for those concepts.
Now a good wall is:
1 ) a lot of layers on both sides (increased mass - the exact relative effect can be calculated with my files)
2) a cavity as large as possible (weakened spring - the exact relative effect can be calculated with the same mass-spring file)
3) If using wooden studs, disconnect them with RC on ONE SIDE ONLY. If doing on both sides and making your wall theiretically more perfect THAT'S A DISADVANTAGE, since then you loose the damping of the system causing the "fo" to become TOO DEEP, making the wall WORSE.
4) try to limit the coincidence dip a bit, but DO NOT EMPHAZISE THIS TOO MUCH, since music noise is as overall insulation hardly improved by maximizing this phenomena.
THe ways you can do that depends on the number of layers. Take panels with different thicknesses with each there own coincidence frequency. This will cause a damping of this dip by dismatching bendingwave lengths.
It's enough that you put a 6 mm or 9 mm panel in-between, on the outside or whatever.
ANY FURTHER IMPROVEMENT will NOT show in the overal TL.
I even do not believe that this special screws to connect gyproc to one another rather then to wooden studs is an advantage when one side is disconnected by RC.
It even can be a disadvantage: if this stiffens the panels too much by acting as a single leave causing the coincidence to lower again.
Best regards
Eric,
This isn't complete, but to time consuming.
Basically a good wall is a simple one, all the rest is magic.
If I should build it for myself now:
With metal studs:
Direct connection to studs
filling with something as 702 (not 703).
Number of layers and cavity depending on insulation I need.
Thickness of at least one board on both sides strongly deviating from the others e.g. a 1/4 or 3/8" panel.
Both sides symetrical or not (doesn't matter that much)
With wooden studs:
The same but one sided with RC or comparable
If using RC I should do the side without RC at a spacing 16"
If I should want to have a havier wall I use staggered studs or independent frames at ca 16" OC
Eric
PS: PLay with the acoustic selector Excel file.
You can alter the TL values from existing BORAL measurements, to imediately see what the effect is on the overal insulation.
You you can check yourself the effect of excluding or reenforcing the coincidence dip, highering or lowering the mass-spring dip etc.
[/quote]