Reflections characteristics of the table top
According to AES information document
Measurement
First of all we covered the table with a layer of sound absorbers, put the microphone directly on top of it and used the small loudspeaker hanging above the table. Its distance to it was measured (127 cm). This first set up aimed at getting a direct sound measurement. For this we measured the impulse response and selected a 2ms snippet of this response. We did all this trying to avoid as best as we could the scattering from the edges of the table and the absorbing layer.
After that we removed the absorber and measured the reflection properties of the hard table surface, using the microphone at the position on the normal to the table top surface (i.e. the 0 degree position). We had to figure out the part of the impulse response that corresponds to the reflection of the table and use the same window length as before.
Matlab code: reflection.m
However, when visualizing our results, we had to conceive that they are quite bad. We couldn't see any clear reflection peaks on the impulse response. So that we could still do the task we were asked to do, Group 1 gave us the permission to use their results for the first measurements. Before applying the 2ms snippet on the impulse responses we get, for the first measurement (the direct sound):
Figure 1: Impulse Response of direct sound, with absorber on table top
and for the 2nd measurement (with reflection on the table top):
Figure 2: Impulse Response of direct+reflected sound, without absorber on table top
We can clearly recognize the first peak which represents the first reflection of the sound wave on the table top. It happens at around 6ms. So it gets easier to see where the snippet must be applied.
We chose to start them at 1.61ms (direct sound) and 5ms (reflected sound).
Compensation
In order to get the characteristics of the table top, we first had to compensate the results from the previous measurement with regard to the distance difference. As we used the results from Group 1 we had to change the distances of direct and refelcted path, as they didn't have the same measurement set up as we had. For instance, they did their direct sound measurement with the microphone hanging at the 0 degree position, while we positionned it directly on top of the absorbing material. Thus the first distance (loudspeaker - microphone) is not 127cm, but 62cm. The compensation will be done with the distance of the first measurement (r1=0.62) and the difference between direct and reflected path of the second one (r2=1.32=mic -> table -> mic): r1/(r1+r2).
After applying the Tukey window, increasing the frequency resolution, applying the time snippet and the FFT we can directly compare the direct and the reflected sounds (not forgetting the scaling):
Figure 3: Frequency Response of Direct and Reflected Sound.
We have quite similar spectra for the direct and the reflected sound. For instance there's a clear peak at around 1.7 kHz. Except in the frequency range of 700 Hz- 1.5 kHz where the direct sound curve is much smoother than the reflected one, the levels never differ of more than 3dB.
Finally we substract the spectra from the two measurements and we get the characteristics of the table top:
Figure 4: Characteristics of the table top.
Over the whole frequency range the direct and reflected sound seem to have the same importance in level, even if for some frequencies the one or the other dominates.