In simulation of a dynamic problem by computer, dynamic equilibrium equations are solved by the finite element methods. These methods estimate the solution on simple and small area of solution domain. In the last two decades, many researchers attempted to avoid meshing. These efforts lead to some unsuccessful methods such as mesh free Galerkin method and successful methods with simple and fixed grids such as extended finite element method and the finite cell method. Improve in the response accuracy of finite element method in dynamic problems is one of the main goals of these researches. The smoothed finite element method and Edge-base Smoothed finite element method are two verified finite element methods suggested to improve the accuracy of results and reduce the computational cost. So, the wave propagation phenomena is the most important dynamic problems in different engineering disciplines. To simulate the wave propagation problem, one of the most popular approximate methods is the ?nite element method (FEM). At high frequencies, when the wavelengths become very small, low-order FEM (h-FEM) may become inappropriate because the number of the elements that can estimate response accurately becomes too large and therefore the computational cost will be very expensive. Furthermore, numerical inaccuracies arise at higher frequencies. In this research, the high frequency wave propagation is simulated by the finite cell method. In simulation of the discrete wave propagation using high-order finite element methods, a new time integration method is proposed to remove the spurious oscillations before and after the wave tip. To demonstrate the ability of the proposed method, results were compared with analytical response. In the next section, using the new version of finite cell method where the B-spline functions is used, mass and stiffness matrices have been extracted and then time-dependent equilibrium equations are solved using existing methods for solving differential equations. To verify results, responses are compared to the responses obtained from the spectral element method with very fine mesh and high degree of shape functions. Key Words: Wave propagation, B-spline and NURBS shape functions, The finite cell method, High order finite element method, Implicit and explicit numerical integration, Spurious oscillations, Dispersion error.