A wave number method (WNM) was proposed to deal with the steady-state mid-frequency acoustic problem. Based on an indirect Trefftz approach, the dynamic pressure response variable was approximated by a set of wave functions, which exactly satisfied the Helmholtz equation. The set of wave functions comprised the exact solutions of the homogeneous part of the governing equations and some particular solution functions, which were derived from the external excitations. The coefficients of the wave functions could be obtained by enforcing the pressure approximation to satisfy the boundary conditions, on which the weighted residual formulation was applied. The results show that the WNM can obtain the same accuracy and convergence as the BEM with less degrees of freedoms.