We measured the acoustic properties of ice-bearing sand packs in the laboratory using a novel acoustic pulse tube within the frequency range of 1-20 kHz, similar to sonic well-logs. We analysed how wave velocity and attenuation (the inverse of quality factor) change with ice saturation during melting. We found strong frequency-dependent correlations for both acoustic parameters with ice saturation. For any frequency within the studied range, velocity decreases and attenuation increases as the ice melts. We used two-phase and three-phase rock physics models to assess our experimental results, and the comparison highlights the influence of ice formation location, sediment frame permeability, and gas content on both velocity and attenuation. Our results pave the way for monitoring ice saturation from sonic measurements as ice saturation has contrasting effects on velocity and attenuation and the effects vary with frequency. Overall, this research contributes to a better understanding of the acoustic response of ice-bearing sediments and provides valuable insights for various applications, including permafrost monitoring and gas hydrate dissociation studies.