Directivity of Scatterers and Absorbers
According to AES information document
Scatterers
Some prisma shaped scatterers were placed on the table top and the scattered sound were measured using a small microphone at various positions relative to the normal to the table surface: 0, 10, 20, 30, 40, 50, 60, 70 degrees of reflection.
The AES standard says that one should do those measurements in an anechoïc chamber to avoid errors caused by sound-reflecting objects. But since the scatterers are small and the room quite big the measurements could be considered as reliable anyway.
Figure 1: Set up with scattering devices
On the picture above one can see the eight microphone positions and the scatterers on the table. Several small devices like this were placed randomly on the table to scatter the sound coming from the loudspeaker on the top. A thin damping layer was stuck around the hanging loudspeaker to have a better direct incoming sound. We have to remember that our own measurement was done without the absorbing layer below.
Like in the first part, where we figured out the reflection characteristics of the table, we studied the impulse response and cut out 2ms long snippets in order to have the direct and the reflected sound. On the following figure, for instance, we can see the impulse response which was measured at the microphone at 0 degrees. In order to set the 2ms snippets the maximum values of each of the direct et reflected "path" were localized and the beginning of the window was set less than one milisecond before.
Matlab code: snippet.m
Figure 2: Time signal with snippets for direct and reflected sound
Then again, doing the whole signal processing as in the first part, we get the frequency response function of the scatterers (not forgetting the compensation of the direct sound and the scaling). Meanwhile we must not forget the fact that there is a time delay between the different microphone positions when the direct and the reflected sound hit them. So this time delay can be used to determine the distance difference between direct and reflected path.
We can now compare the direct to the reflected sound.
Matlab code: scatterers.m
Figure 3: Direct and reflected sound
We can see that the direct sound has a much smoother curve than the reflected one. They have the same peak at 1700 Hz and both have a small increase at 500 Hz. The levels are, for both paths, very very low. There might be some error which was done during the measurement. Nevertheless, it is not the level of each path that is of interest but the difference between both, so that we can get the directivity of the scatterers. The levels are approximately the same. That's why, when we substract both levels, we get results around zero:
Figure 4: Difference between direct and reflected sound --> frequency response of the scattering surface
The big peaks are a consequence of the huge dips which represent the frequency response of the reflected path at certain frequencies.
Directivity of the Scatteres
The goal of this part of the lab is to get the directivity of the scatterers.
We chose to put on zero the lowest value in dB in order to have nice directivity plots:
Figure 5: directivity plots for the third octave frequency bands
As one can see the scatterers create a different frequency response spread over the angles (0 to 70). However one can point out that there are some angles welcoming most of the energy at a certain frequency. It seems also that for the fequencies close to each other, the energy has approximately the same directivity.
Finally the scatterers played quite well their role. The sound is well scattered if its energy is spread out over every angle.
Absorbers
The same measurements were performed but instead of scatterers several sound absorbing patches were randomly distributed on the table.
Figure 6: Measurement set up with small absorbing patches (photo retrieved from group 1)
Again, our results are for a measurement set up without the big absorbing panels below.
We proceed exactly as we did for the scatterers. First we do the snippetting,
Matlab code:snippet_abs.m
Figure 7: time signal with snippets for direct and reflected sound
and the signal processing:
Matlab code:absorbers.m
Figure 8: direct and reflected sound
When looking at the figure above there is to say that the direct sound shows, most of the time, a bigger level than the reflected one. This would be logical as part of the sound energy gets lost in the absorbing panels.
Figure 9: Difference between direct and reflected sound --> frequency response of the absorbing surface
Again, here we have a logical consequence of the sound absorption. The frequency response is nearly always positive in dB. The dips correspond to the frequencies the most absorbed by the absorbers.
Directivity of the Absorbers
For all third octave bands the directivity of the absorbers is plotted.
Figure 10: Directivity plots for the third octave frequency bands
The directivity of the absorbers is totaly different from the one obtained with the scatterers. One can't say that there are angles where the energy is mostly located. Besides there is not such a difference of angle between the frequencies. The main difference here between the frequencies is the overall value. As one knows the absorbers are always better in a specific frequency range. Here we used porous absorbers so they should be better in high frequencies. But this effect can be even better seen in figure 9.
Conclusion
The directivity of the sound depends a lot on what encounters the sound. If one wants to use scatterers with a different shape, one will have different results.
One thing which could maybe improve the results and the interpretation is to put damping layers beloy the devices under study. In that case one won't have to take the reflection of the table into consideration and have only the "real" reflection thanks to the scatterers.