A　space-time　coupled　spectral　element　method　based　on　Chebyshev　polynomials　is　presented　for　solving　time-dependent　wave　equations.　Acoustic　propagation　problems　in　1　+　1,　2　+　1,　3　+　1　dimensions　with　the　dirichlet　boundary　conditions　are　simulated　via　space-time　spectral　element　method　using　quadrilateral,　hexahedral　and　tesseractic　elements　respectively.　Space-time　coupled　spectral　element　method　can　obtain　high-order　precision　and　the　dispersion　is　stable　over　time.　With　the　same　total　number　of　grid　nodes,　higher　numerical　precision　is　obtained　if　the　higher-order　Chebyshev　polynomials　in　space　directions　and　lower-order　Chebyshev　polynomials　in　time　direction　are　adopted.　When　space-time　coupled　spectral　element　method　is　used,　time　subdomain-by-subdomain　approach　is　more　economical　than　time　domain　approach.