Acoustic Switch Device for a Splitter Acoustic Wave made by Waveguides and Resonator

In this paper, we present the propagation of acoustic waves in switchable device within a specific reduced frequency range. Our proposed system comprises an input and three output lines (three channels), initially acting as an amplitude divider that splits an incident acoustic wave into three output channels. We demonstrate theoretically that the introduction of a resonator of length $d_{2}=0.5 \mathrm{D}$ along the waveguide of length $d_{c}=0.5 \mathrm{D}$ connecting the output channels to the input channel of our system, efficiently modulates the acoustic signal on the reduced frequency range $\Omega=[2.2-4.0]$. Consequently, the input signal is entirely transmitted at the first output line ($\mathrm{T}_{1}=1$), while transmissions through the second and third channels, as well as reflection, are nullified ($T_{2}=T_{3}=R=0$). The theoretical analysis is based on the Transfer Matrix Method (TMM), enabling us to determine the three transmission rates $T_{1}, T_{2}, T_{3}$, and the reflection rate R. The length and position of the resonator control the acoustic wave, achieving an acoustic switching phenomenon with important efficiency.