build your own cabinets, which material?

Some detailed explanations to the question of "what kind of material for my cabinets": I hope it will be of interest to some people:

Sound (energy) from inside the speaker cabinet should not get through the walls of the cabinet and be heard outside. The weighed sound-transmission factor is a measure of how much the walls will "filter" out from getting through, ie the higher this factor the better.

The weight per square metre [m“] of a wall with 10kg/m2 for example has around 30dB weighed sound-transmission factor for most materials (with few exceptions). Interestingly a wall with 50 kg/m2 has insignificantly more weighed sound-transmission factor and a wall with 100 kg/m2 has around 36dB. So by increasing the weight per area by a factor of 10 the weighed sound-transmission factor increases only by 6dB. Whereas a wall with 1 kg/m2 in contrast has only 20dB weighed sound-transmission factor, which is 10dB less than 30dB of the first example.
That means that when increasing the mass over 10kg/m2 the gain is relatively small.
This is when sandwich walls come in as a good alternative.

It is important to state that the weighed sound-transmission factor is dependent on the frequency and therefore differs significantly over the frequencyband.
There are 3 main frequency ranges of importance:
1.) low frequencies (bass) where the weighed sound-transmission factor is mainly depending on the weight per area [m“] (see examples above). The formula to calculate the weighed sound-transmission factor is according to Heckl/Mueller (P.436):
R = (20*lg{pi*f*m''/ (p* c)} - 3) dB
with p(roh) = densitiy of the air and c = speed of sound in air

2.) A second frequency range where the velocity of sound in the wall is similar to the speed of sound in air and the weighed sound-transmission factor is dramatically reduced (resonance). This frequency can be calculated according to L.Cremer (p.81-104):
fg= c2/ (2pi) *sqrt(m''/B)

or fg= 640000* sqr(P/E) / h
with P (roh) = density of the wall, E = E-module of the wall and h the thickness and B the stiffness of the wall.

This frequency would be around 1000Hz for a plywood with 20mm thickness (if you look at the formula above you see that doubling the wall thickness will half this frequency to 500Hz) This is a critical frequency band since the ear is very sensitive around this frequency. Using 20mm of hard fibreboard will bring the frequency to 2000Hz (still critical frequencyband) and 20mm of heavy concrete will produce a frequency of 700Hz. Using 10cm of concrete would result in a frequency of 150Hz. This is an area where the ear is not so sensitive but where most of the fundamental frequencies in music are and therefore a lot of energy. Making the concrete wall even thicker brings the coincidence frequency into the bass range and can results in a ringing and booming bass if the cabinet walls are rather large! (Have you noticed in concrete buildings with thick walls how well the bass of the neighbours music can be heard in the flat next door?)
The “dip” in the weighed sound-transmission factor is more or less dramatic depending on the ratio of the dimensions of the wall to the wavelength of the coincidence frequency,
Or length/lamda(g) should be small. Example for a coincidence frequency of 1000Hz the wavelength would be 0.34m, therefore the wall dimensions (in any direction) should be less than 340mm. To be on the save side this should be 170mm and less. This can be achieved by bracing, which effectively decouples on part of the wall from another. So the bracing should be in distances of 170mm in this case of 20mm thick plywood.


3.) The third (and highest) frequencyband is above the coincidence frequency and can be calculated according to Heckl/Mueller (p.438):

R= 20*log (pi*f*m''/{p*c}) - 10 lg {1/(2*n) *sqrt(fg/f)}
With n = loss factor

This means that the weighed sound-transmission factor will increase by 8dB per octave (25dB per decade); i.e. the higher the frequency the less sound transmission.

By the way it has to be stressed that the less sound transmission through the wall the more reflection inside and therefore more internal resonances! These resonances however can be effectively dampened by absorption material such as wool in the centre of the speaker cabinet (not the walls!)
It is also important to note that these calculations apply to the sound in air inside the cabinet that are converted into vibrations in the wall and then converted back into sound on the outer side of the cabinet into the room. There is another form of transmission however where the vibrations of the chassis frame transmit into the cabinet and then into the air. This is a different condition and has to be calculated differently. It is important therefore to acoustically disconnect the driver from the cabinet by soft rubber like materials.

Conclusion: Cabinet walls should have a minimum weight per area of 10kg/m2 to increase the weighed sound-transmission factor but at the same time be stiff.
The material should also have a reasonably high loss factor (not the case in glass for example).
Large walls can be decoupled by bracing to decrease the dip at the coincidence frequency.

As to the sandwhich cabinets: sand as a filler is a good idea because it has a high loss factor and a high weight. As an easier (lighter) alternative you could use rubber granulate or if you want even lighter: wool. Sheep wool is much better (on the inside of the cabinet too) than polyester wool or glassfibre (pink batts) and easily available in New Zealand (as heat-insulation material). Should be available in other countries too though.

All in all please keep in mind that the most important part is still the driver (mainly the cone)! A crappy driver is still no use in a perfect cabinet, but an excellent driver in a mediocre cabinet can sound extremely well! So I would not spend a fortune of money (or time) on a 100kg cabinet with $20 drivers from east asia. This is of course no news but some people seem to forget this nevertheless. (when I was 16 I did that as well and filled cabinet walls with tons of sand!)