Abstract:Using the wave superposition theory,the transmittance formula of SH wave is derived in 1D finite number cycles phononic crystal,and the wave superposition theory is established.The comparative study on the wave superposition theory and the transfer matrix theory are carried out.The results show that the two methods are same.The wave superposition theory has advantages of the numerical calculation of the transfer matrix theory,while overcomes the disadvantages of the transfer matrix theory which can not interpret the cause of generating the energy band.Thus the wave superposition theory is a better way to study SH wave energy band in 1D finite number cycles phononic crystal.