Utilizing textile-based acoustic materials can be considered basically from two points of view. First, it may be used as a sound absorbing material. Second, it may be used as a decoration that gives the surrounding area a new artistic appearance. To improve the acoustic possibilities of any woven fabric, it is necessary to study the influences of yarn characteristics and the internal structures of weave interlacement. To understand the impact of the yarn on the fabric, the samples were prepared using only polyester fiber as textured, twisted, and staple yarns. Regarding this experiment, the basic weave’s structure type, such as plain, rib, sateen, and twill, were used. Overall, 16 woven fabrics were prepared. The investigation was performed in the range of low to medium acoustic frequencies. The experiments were conducted in an anechoic chamber. Compared to other yarn types, fabrics formed from textured polyester yarn had higher sound absorption properties. Moreover, the observed results show that the different incidence angles of acoustic signals influence the measured sound absorption properties of a textile.