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The current work analyzes the transmission behavior of plane harmonic waves in an isotropic medium. The observation is made for homogeneous type solid in the context of generalized dual phase lag model of thermoelasticity. Concept micro-temperature, where the microelements have different temperatures has also been considered. The basic focus of thework is to predict the influence of initially applied magnetic field on plane waves through the elastic solid. We have made an attempt to find exact solution of the problem using an analytical technique of a normal mode analysis method. The theoretical results are obtained for a generalized solid in order to test the numerical calculation of a magnesium crystal. It is found that the magnetic field reduces the strength of the attenuation factor.