High-frequency noise exceeding 1 kHz has emerged as a pressing public health issue in industrial and occupational settings. In response to this challenge, the present study explores the development of a graphene oxide–polyethyleneimine (GO-PEI) foam (GPF) featuring a hierarchically porous structure. The synthesis and optimization of GPF were carried out using a range of analytical techniques, including Raman spectroscopy, scanning electron microscopy (SEM), Braunauer–Emmett–Teller (BET) analysis, X-ray diffraction (XRD), and Fourier-transform infrared spectroscopy (FT-IR). To evaluate its acoustic properties, GPF was subjected to sound absorption tests over the 1000–6400 Hz frequency range, where it was benchmarked against conventional melamine foam. The findings demonstrated that GPF with a GO-to-PEI composition ratio of 1:3 exhibited enhanced sound absorption performance, with improvements ranging from 15.0% to 118%, and achieved a peak absorption coefficient of 0.97. Additionally, we applied the Johnson–Champoux–Allard (JCA) model to further characterize the foam’s acoustic behavior, capturing key parameters such as porosity, flow resistivity, and viscous/thermal losses. The JCA model exhibited a superior fit to the experimental data compared to traditional models, providing a more accurate prediction of the foam’s complex microstructure and sound absorption properties. These findings underscore GPF’s promise as an efficient solution for mitigating high-frequency noise in industrial and environmental applications.