In order to research the rules of wave transmission and reflection on rough interface,on the base of classical Cantor ternary set,author extends the interface model of Cantor set,presents a method to calculate fractal dimension in theory.Based on the theory of one dimensional stress wave and making use of mathematics induction method from the specific to the general,theoretical relation between fractal dimension of extended Cantor set and the transmission and reflection coefficients of wave when wave transmits across the interface is deduced austerely.