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Theory of resonant sound transmission through small apertures on periodically perforated slabs

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1 Author(s)
Wang, Xinlong ; Key Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing 210093, China

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An analytical theory for sound transmitting through apertures that are slits or holes periodically pored on one- or two-dimensional rigid panels is developed in small-aperture approximation, with all coefficients of reflection and transmission given explicitly in concise and easily calculable forms. We utilize acoustical impedance to quantitatively describe the effect of sound diffraction by both surfaces of a perforated slab on the aperture resonance. We show that diffraction induced reactance Xa, which is acoustically inertant (Xa>0) for incident wavelength λ longer than the period Λ of the perforated slab, can become infinitely large as λ approaches to Λ. We further show that the singularity of Xa not only causes the already known full reflection of acoustic waves at λ=Λ, but also drastically changes the aperture resonance leading to the extraordinary acoustical transmission that was observed in recent experiments. With this understanding, tuning the resonant transmission becomes practically feasible in applications of the resonant transmission phenomenon.

Published in:

Journal of Applied Physics  (Volume:108 ,  Issue: 6 )