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We have investigated the spin wave modes of dipolar coupled, highly shape anisotropic magnetic nanoislands forming square artificial spin ice system by performing micromagnetic simulations using MuMax3 in combination with Matlab coding. Here, artificial spin ice is considered to be formed by the four identical square ring-type structure of elliptical shaped nanoislands of permalloy. Our results demonstrate a direct relation between the spin wave modes generated and the micro-states formed in the system. Thus, we show that single ring type structure may alone be adequately used to understand the spin wave modes of square artificial spin ice.