Density (rho) and speed of sound (u) of a cationic surfactant, DTAB (dodecyltrimethylammonium bromide) in aqueous solutions of tetraalkylammonium bromide, R4NBr (R= propyl, butyl, and pentyl) have been measured in the temperature range (293.15-318.15) K at an interval of 5 K. The temperature dependence of speed of sound has been used to compute the critical micelle concentration (CMC) and second critical micelle concentration (2nd CMC). Various volumetric and compressibility parameters have been evaluated in micellar and postmicellar regions to investigate the behavior of elongated micelles in comparison to the spherical ones. The trends of all these parameters have been examined in terms of a competing pattern of various intermolecular interactions existing in the ternary (tetraalkylammonium bromide + water + surfactant) system. The hydrophobic hydrophobic interactions show the predominance in the studied system, which is enhanced with the increase in the alkyl chain length of the bromide salt.