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We study the transmission coefficient of a plane wave through a 1D finitequasi-periodic system -- the Frenkel-Kontorova (FK) model -- embedding in aninfinite uniform harmonic chain. By varying the mass of atoms in the infiniteuniform chain, we obtain the transmission coefficients for {\it all}eigenfrequencies. The phonon localization of the incommensurated FK chain isalso studied in terms of the transmission coefficients and the Thoulessexponents. Moreover, the heat conduction of Rubin-Greer-like model for FK chainat low temperature is calculated. It is found that the stationary heat flux$J(N)\sim N^{\alpha}$, and $\alpha$ depends on the strength of the externalpotential.Comment: 15 pages in Revtex, 8 EPS figure

Wave transmission, phonon localization, and heat conduction of a one-dimensional Frenkel-Kontorova chain