Optimal size design of Fabry–Pérot sound absorbers based on the loss equation

Aiming at the problem of the need for trial-and-error in the design of the size of Fabry–Pérot (F–P) resonant absorbers, we start from the sound absorption caused by loss and propose a design method to accurately obtain the optimal size of F–P tubes with circular and rectangular cross sections. An innovative loss equation is constructed, which relates the F–P tube's critical loss to the transmission loss of sound waves in the tube. By solving the loss equation, the size of the F–P tube required for perfect sound absorption can be obtained. This method avoids the need for experiments or simulations to find the optimal size, and it is simple, fast, and accurate. Single-frequency perfect sound-absorbing metasurfaces of circular and rectangular cross sections were designed using this method. The performances of these metasurfaces were verified using theoretical, numerical, and experimental models. The three resulting sound absorption coefficient curves had good consistency and achieved perfect sound absorption at the target frequency. The feasibility and accuracy of the design method were established. The essence of the loss equation is to find the size of the F–P tube corresponding to the “zero” point on the real-frequency axis of the complex-frequency plane. The work in this paper is of guiding significance for determining the sizes of F–P tubes.