We have seen that the bandwidth of high absorption is proportional to the airspace depth, h. If only a restricted depth is available, and we wish to achieve reasonably high absorption over a wider band, we must design a number of tuned resonant absorbers having different resonance frequencies to cover the whole required frequency range:
f2- f1 = n 6fH
in such a way that, for every frequency, a reaches near to amax on at least one partial surface area.
However, further analysis shows that the necessary construction volume remains the same: what we save in depth of air cushion must be made up in additional area of absorptive surface.
In each case, the choice depends on the available space. Certainly, it is more expensive to enlarge the treated area than to increase the depth of the treatment, so h should be chosen as great as the available space will allow.
The choice of flow resistance for the filling material is not quite so straightforward as it seemed when we were cohsidering only the sound absorption at the resonance frequency. Certainly, it would not be favorable to choose R smaller than pC, because then we would decrease both the maximum absorption at resonance and the width of the absorption curve (Fig. 26).
But if R is greater than pc, then again the maximum absorption at resonance decreases, but we get a broader curve, which may be desirable. If we try to optimize both the maximum absorption at resonance and the half power bandwidth, by forming their product:
Xmax ~fH = 27f[ 4(R/pc)/(I + R/pC)](h/C)fR2
we see that it would still be good to choose a large value for R.
However, even a choice of infinitely high R would yield a result for the product that is only twice that for the matching case, R/pc = I. And if we make R too great, we invalidate our whole theory of resonating absorbers: a too-strongly damped resonator is no resonator at all!
We conclude, then, that a choice of R/pc around 2 to 3 will give the best compromise between a high maximum sound absorption at resonance and a broad half power bandwidth.
In Part One, we presented several examples (#4 - #7) in which we calculated the resonance frequency for differert combinations of perforated metal sheet and airspace (pp. 23-28). We return to those treatments now to determine the half-power bandwidths and to see the effect of different choices of filling material.
