This paper describes a method to suppress emergence of an acoustic shock wave and also to damp pressure waves in a tunnel generated by entry of a high-speed train. It exploits both action of wave dispersion and damping by connecting a double array of Helmholtz resonators to the tunnel axially. Emphasis is placed on difference in mechanisms of suppression of shock and of damping of pressure waves. Using the nonlinear wave equations derived previously, the numerical calculations are carried out to examine the effects of the double array. There are two important parameters called the coupling and tuning parameters characterizing each array. It is shown that the double array acts very effectively when the tuning parameter of one array is set to be 10 or higher than it for suppression of shock and the one of the other array is set around unity for damping of pressure waves, while the coupling parameters of both arrays are chosen to be unity.
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