In this paper we present experimental investigation of the frequency dependence of nonlinear elastic (Murnaghan) moduli of polystyrene samples by the ultrasonic method based on the acousto-elastic effect. Measurements were performed in a wide frequency range, from 250 kHz to 2.5 MHz. The absolute values of the Murnaghan moduli demonstrated considerably nonlinear dependencies on the ultrasound frequency. While at higher frequencies above similar to 600 kHz no significant variations of the moduli occurred, at lower frequencies a drastic rise of absolute values in several orders of magnitude has been observed. The values obtained at lower frequencies were utilized for theoretical estimation of parameters of a strain solitary wave in this material. The data obtained correlated well with the parameters obtained experimentally and allowed for explaining the long-lasting discrepancy between theoretical estimations and experimental results.