Sound Transmission Through a Slitted Wall at Non-Continuum Conditions

This talk presents a study of the transmission of sound waves through periodically slitted walls in regimes where the characteristic aperture size and acoustic wavelength are comparable to the molecular mean free path of the gas. The acoustic field is generated by small-amplitude normal oscillations of a vibrating wall located upstream of the perforated plate.
The problem is investigated across the full range of gas rarefaction rates, combining free-molecular and continuum-limit analyses with direct simulation Monte Carlo (DSMC) calculations.
The results indicate a qualitative transition in the directivity of the acoustic field with gas rarefaction. Under free-molecular conditions, the transmitted field is strongly anisotropic, owing to geometrical filtering of molecular velocities by the slits. In the continuum limit, collisions promote isotropy in the molecular velocity distribution, such that each slit behaves as a localized mass monopole source.
In cases where the wall slits are sufficiently close, non-monotonic variations in transmission with slit spacing are observed, representing Rayleigh’s anomaly, which gives rise to extraordinary transmission.
This behavior is consistently captured by both DSMC simulations and continuum-limit predictions.
Multi-slit interactions are attenuated strongly by rarefaction, and extraordinary transmission is not observed at highly rarefied conditions.

This work is towards an M.Sc. degree under the supervision of Assoc. Prof. Avshalom Manela of Aerospace Engineering, Technion. Coadvisor: Dr. Yaron Ben-Ami, Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford.