This study presents an acoustic membrane design utilizing a thin foil sound resonance mechanism to enhance sound absorption and insulation performance. The membranes incorporate single-layer and double-layer structures featuring parallel foil square wedge-shaped coffers and a flat bottom panel, separated by air cavities. The enclosed air cavity significantly improves the sound insulation capability of the acoustic membrane. Parametric studies were conducted to investigate key factors affecting the sound transmission loss (STL) of the proposed acoustic membrane. The analysis examined the influence of foil thickness, substrate thickness, and back cavity depth on acoustic performance. Results demonstrate that the membrane structure enriches vibration modes in the 500–6000 Hz frequency range, exhibiting multiple acoustic attenuation peaks and broader noise reduction bandwidth (average STL of 40–55 dB across the researched frequency range) compared to conventional resonant cavities and membrane-type acoustic metamaterials. The STL characteristics can be tuned across different frequency bands by adjusting the back cavity depth, foil thickness, and substrate thickness. Experimental validation was performed through noise reduction tests on an air compressor pump. Comparative acoustic measurements confirmed the superior noise attenuation performance and practical applicability of the proposed membrane over conventional acoustic treatments. Compared to uniform foil resonators, the combination of plastic and steel materials with single-layer and double-layer membranes reduced the overall sound level (OA) by an additional 2–3 dB, thereby offering exceptional STL performance in the low- to medium-frequency range. These lightweight, easy-to-manufacture membranes exhibit considerable potential for noise control applications in household appliances and industrial settings.