For locally periodic multiscale wave equations,we solve the high dimensional multiscale homogenized problem obtained from multiscale convergence that contains all the microscopic and macroscopic information.We consider the sparse tensor product finite element method which achieves an accuracy essentially equal to that for the full tensor product,but only requires an essentially equal number of degrees of freedom as for solving a one macrosocopic scale wave equation.(Joint work with Bingxing Xia,NTU,Singapore).