In the last decade, various asphalt paving materials have undergone investigation for sound attenuation purposes. This research aims to delve into the innovative design of sustainable road pavements by examining sound absorption in rubber-modified asphalt mixtures. More specifically, the impact of alternative sustainable materials on the sound absorption of asphalt mixtures across different temperatures, precisely crumb rubber (CR) derived from recycling of end-of-life tires, was investigated. The acoustic coefficient and its Gaussian fit parameters (Peak, BandWidth, and Area Under the Curve) were evaluated. Five different types of asphalt mixtures were studied, encompassing dense, discontinuous, and open mixtures with 0%, 0.75%, and 1.50% CR incorporated through the dry process (DP). The results of sound absorption indicated a slight influence of crumb rubber at temperatures ranging from 10 °C to 60 °C, particularly in mixtures with high void content. On the other hand, as expected, the void content proved to be highly correlated with sound absorption. These findings facilitated the establishment of predictive models that correlate acoustic absorption spectra with the characteristics of asphalt mixtures. As a result, these models will be valuable in the design of the next generation of sound-absorbing pavements.