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We investigate the phonon spectra of two-dimensional liquid dusty plasmas ona one-dimensional periodic substrate using numerical simulations. Thepropagation of the waves across the potential wells of the substrate isinhibited due to the confinement of the dust particles by the substrate minima.If the substrate wells are narrow or deep, one-dimensional chains of particlesare formed in each minima, and the longitudinal motion of an individual chaindominates the propagation of waves along the potential wells of the substrate.Increasing the width or decreasing the depth of the substrate minima allows theparticles to buckle into a zig-zag structure, and the resulting spectra developtwo branches, one for sloshing motion and one for breathing motion. Therepulsion between neighboring dust particles produces backward propagation ofthe sloshing wave for small wave numbers.

Phonon spectra of two-dimensional liquid dusty plasmas on a one-dimensional periodic substrate