Figure 4

(a,b) Normalized surface acoustic resistance \({\text{Re}} \left( {z_{s} } \right)\) and reactance \({\text{Im}} \left( {z_{s} } \right)\) of the metamaterial with and without rubber coating, where \(z_{s} = Z_{s} /Z_{0}\). The solid lines and circles represent theoretical predictions and finite element (FE) simulation results, respectively. Colored arrows indicate the absorption peak frequencies. (c–e) The effective sound speed \(c_{z}\) on the water channel with different isotropic loss factor \(\eta_{r}\), channel width \(w\) and the thickness of rubber coating \(t_{2}\). Other parameters are consistent with those in Fig. 2a. The red solid lines represent the real part of \(c_{z}\), and the blue solid lines represent the imaginary part of \(c_{z}\).