<p>We present the results of experimental and theoretical studies on the effect of a strong pump wave on a weak probe wave in an acoustic rod resonator (with rigid and soft boundaries) made of annealed polycrystalline copper. The measurements were carried out with simultaneous excitation of the resonator in its first and fourth longitudinal modes. An analytical description of nonlinear effects (changes in the amplitude and frequency of resonant oscillations for a weak wave under the influence of a strong one) is developed within the framework of the hysteretic equation of state for a polycrystalline solid with saturation of amplitude-dependent internal friction. By comparing the experimental and analytical amplitude dependences of the nonlinear effects, we determined the parameters of the hysteresis nonlinearity of annealed copper for various combinations of strong and weak wave frequencies corresponding to the first and fourth resonator modes.</p>