Both the ultrasonic velocity at 3 MHz and the absorption coefficient in the frequency range from 0.2 to 2 MHz were measured for aqueous solutions of poly(sodium 4-styrenesulfonate) over the concentration range from 5 to $25\%$ (by weight). The pulse echo overlap method was employed to measure the ultrasonic velocity over the temperature range from 10 to $90^{circ}C;$ the high-Q ultrasonic resonator method was used for the measurement of the absorption coefficient at $20^{circ}C.$ The velocities exhibited their maximum values at ca. 55, 59, 63, 67, and $71^{circ}C.$ for the 25, 20, 15, 10, and $5\%$ solutions, respectively. The velocity increased with respect to the poly(sodium 4-styrene-sulfonate) concentration at a given temperature. A study of the concentration dependence of the both the relaxation frequency and amplitude indicated that the relaxation at ca. 200 kHz is related to structural fluctuations of the polymer molecules, such as the segmental motions of the polymer chains and that the relaxation at ca. 1 MHz resulted from the proton transfer reactions of the oxygen sites of $SO_3.$ Both the absorption and the shear viscosity increase upon increasing the polymer concentration, but they decrease upon increasing the temperature.