Since society is moving towards sustainable development, interest in secondary use of waste has recently become significant. This paper investigates a process to develop an acoustic material, using two types of waste. Composite acoustic panels were developed using waste tyre textile fibres (WTTF) and paper sludge (PS), and polyvinyl acetate (PVA) were used as a binder. Non-acoustic (bulk density, airflow resistivity) and acoustic (sound absorption coefficient, sound transmission loss) parameters were studied. Composite acoustic panels with different proportions of WTTF/PS/PVA (sixteen samples) were subjected to testing for the sound absorption coefficient according to ISO 10534-2 and sound transmission loss according to ASTM E2611. The density of all samples varied between 155.2 and 709.9 kg/m3, the thickness between 14.4 and 20.5 mm, and the airflow resistivity between 29.5 and 101.5 kPa∙s/m2. The results reveal that the proportion of various waste materials in mixtures can improve the acoustic performance of panels. The combination that gives the highest αavg. with a value of 0.50 was experimentally found to be 70% WTTF mixed with 15% PVA and 15% H2O. The average sound absorption coefficient with a value of 0.46 was also found to be 25% WTTF mixed with 25% PS and 25% PVA and 25% H2O. In sound transmission loss, the most effective was 50% PS and the 50% PVA composite, the TLeq was 28.3 dB, while the composites together with 30% WTTF, 20% PS and 25% PVA, and 25% H2O showed 18.9 dB loss. The results obtained using WTTF and/or PS wastes are attractive and show great and promising development potential.