What equipments/instruments do I need to determine the absorption coefficient of a cardboard box? This post is not a duplicate of that post, which is discussing equations, while this post is discussing instruments, such as Decibel meter.
I would like to build a bigger box with 26 smaller boxes, the center is the red 
 square shown as below.

The smaller box looks like this, 40cm*30cm*30cm.

a piece of cardboard which is each facet of the smaller box looks like this

What equipments/instruments do I need to determine the absorption coefficient of the bigger box?
 A: There are specified measurement methods for what you are seeking to achieve. The most well known are described in ISO 354:2003 which describes the measurement of the "random incident absorption coefficient" in a reverberation chamber and ISO 10534-1:1996 and [ISO 10534-2:1996], which describe the determination of the "normal incidence absorption coefficient" with the method of standing wave ratio (ISO 10534-1:1996) and transfer function method (ISO 10534-2:1996) respectively.
In general, for a DIY setup, I believe it would be easier (and most probably more convenient) to follow the diffuse method (ISO 354:2003). In this method, you measure the reverberation time -Wikipedia link- of the room without the material of interest (cardboard in this case), and then with it inside the room and assume that the difference in the reverberation time is caused only by the material introduced in the second measurement. Since you assume that the reverberation time depends on the volume of the room (constant) and the absorption in the room (change only due to the cardboard), you will manage to calculate the absorption introduced by the cardboard. Then you will have to divide that by the surface area of the cardboard exposed to sound (since we assume that absorption is only happening on the surface of the material... Not exactly, but still, you can think of it like that) in order to get the absorption coefficient of the material.
Now, some things to take note of:


*

*First of all, this is going to be a very rough approximation of the material's absorption coefficient since many of the prerequisites for such a measurement are not fulfilled here (diffuse sound field, uniform absorption in the room, etc.).

*You will have to calculate that for many different frequency bands (octave, 1/3 octave, etc.).

*Make sure to measure the whole surface exposed to the sound field. For example if you place one standing cardboard leaf/ply in the room, the surface being exposed is the surface of both sides.

*It would be beneficial to take many measurements (I don't remember by heart, but I believe in the ISO 4 is the minimum, I might be wrong though) and average to get "statistically more meaningful results" (this is in quotes because it is used a bit abusively here). This should be the case for both measurements (with and without the material).

*If you have considerable amounts of absorption in the room, you may find it beneficial to use Norries-Eyering - https://www.cs.tut.fi/~ypsilon/80545/rtnotes.html - formula for reverberation instead of Sabine's - https://www.techglads.com/cse/sem1/sabine-formula-for-reverberation-time/ - (see also an example here -https://www.acousticlab.com/eng/reverberation-time-and-sabine-s-formula.html). I don't have extensive experience with such measurements, so I cannot suggest what the change in the final result will be. As long as I am aware though Norris-Eyering formula is better when the mean absorption coefficient in the room is higher than (roughly speaking) 0.1 (you can have a look at the Prediction of the Reverberation Time in Rectangular Rooms with Non Uniformly Distributed Sound Absorption article by Neubauer and Kostek for more info).

