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We systematically investigate the sound modes of momentum dissipatedholographic systems. In particular, we focus on the Einstein-linear axions andthe Einstein-Maxwell-dilaton-axion theories in four-dimensional bulk spacetimedimensions. The sound velocities of the two theories are computed respectivelyand the sound attenuation of the Einstein-Maxwell-axion theory is alsocalculated analytically. We also obtain numeral dispersion relations in the twotheories which match with our analytical results. Our results show that thesound velocity of the Einstein-Maxwell-dilaton theory with additional linearaxion fields is equivalent to that of 2 + 1 - dimensionalBanados-Teitelboim-Zanelli black holes. It allowed us to compare our solutionof the Einstein-linear axions theory with that of systems without translationalinvariance from another method. After the computation on the sound velocity, wecalculate the quasinormal modes of scalar-type fluctuations in theEinstein-Maxwell-dilaton-axion theory. The results show that a dynamicalinstability is observed under the condition that the null energy condition isviolated.

Sound modes and stability of momentum dissipated black branes in holography