Extraordinary Sound Screening in Perforated Plates

We report extraordinary effects in the transmission of sound through periodically perforated plates, supported by both measurements and theory. In agreement with recent observations in slit arrays, M. H. Lu et al. [Phys. Rev. Lett. 99, 174301 (2007)], nearly full transmission is observed at certain resonant frequencies, pointing out similarities of the acoustic phenomena and their optical counterpart. However, acoustic screening well beyond that predicted by the mass law is achieved over a wide range of wavelengths in the vicinity of the period of the array, resulting in fundamentally unique behavior of the sound as compared to light.

Figure 1

(a) Measured transmission spectra of Al plates for different geometrical parameters, as indicated by labels. For comparison, we show the transmission of a 3-mm thick plate without holes (black solid curve), along with the prediction of the mass law for that plate (black dashed curve). (b) Transmission spectra of the perforated plate with $d=3\mathrm{mm}$, $p=5\mathrm{mm}$, and $t=3\mathrm{mm}$ (solid lines) and the nonperforated plate with $t=3\mathrm{mm}$ (dashed lines) at different angles of incidence.

Figure 2

(a) Filling fraction of perforated plates as a function of $t/p$ and $d/t$. The dots are the coordinates of measured samples (see 11). (b)–(d) Measured [blue (gray) curves] and calculated (black curves) transmission of arrays with different geometrical parameters (see insets). The measurements are for $37\times 14$ holes and the theory corresponds to infinite arrays [27].

Figure 3

(a) Transmittance spectra of 2-mm thick aluminum plates pierced by $39\times 39$ holes of 3 mm in diameter, distributed periodically (black line, for a period $p=5\mathrm{mm}$) and randomly [red (gray) line]. The transmission without holes is shown for comparison [blue (light gray) line]. (b) and (c) 2D Fourier transforms (contour plots in log scale) of the periodic and random arrays, respectively, showing hot spots of the former and a broad distribution of the latter in reciprocal space. The random and the periodic array have the same filling fraction value in order to appropriately compare their transmission features.

Figure 4

Transmission spectra of the $d=3\mathrm{mm}$, $p=5\mathrm{mm}$, $t=3\mathrm{mm}$ perforated plates made of brass, aluminum, and PMMA, compared to theory in the hard-solid limit (black curve).