Analytical Model of a New Acoustic Conductor Lined with Linear Increasing Perforated Area

An acoustic conductor is a simple method of impedance- matching of plane sound waves in pipes. The present work offers a theoretical study of a new design conductor, this conductor is based on a constant cross-section pipe and treated with a linear gradually increasing perforated area along its length. In addition, the study outlines a design procedure for optimizing the conductor performance. The design parameters such as the conductor length, the graduality factor of the perforated area along the conductor pipe, and the conductor cross-section diameter are separately studied in detail for the proposed conductor. The wave equation describing the sound propagation through the conductor is considered, and the solution of this wave equation is derived using the modified Hankle function for a plane sound wave. In general, the frequency dependence of the computed parameters such as the reflection coefficient, the normalized wave resistance, and the normalized wave reactance at the input of the considered acoustic conductor shows a sharp drop frequency, at which the reflection coefficient is less than 0.1, as well as, the wave propagation resistance tends to unity while the reactance tends to zero. The study summarized all designed parameters in one design parameter Ac, named the characteristic area of the conductor. The computed results show that increasing Ac leads to shifting the drop frequency towards low frequencies. This enables the designer to design the official sound conductor for specific applications under the available dimensions. A multiple treatment that gives small graduality and a large perforated area is computed, which provides good matching for the conductor. A reasonable agreement between the obtained results with a previous experimental study in our lab by Shenouda for this new conductor design.