Abstract: The speed of sound in quark matter is an important physical quantity for studying the properties and the spacetime evolution of quark-gluon plasma (QGP). The behavior of the speed of sound with respect to temperature and density can reveal to some extent the equation of state and the phase structure of QGP. Building upon the previous studies on the speed of sound in symmetric quark matter, the formulae for calculating the speed of sound in asymmetric quark matter in the temperature-density space are further derived. The PNJL model is then used to calculate the dependence of the speed of sound on isospin asymmetry. Furthermore, the relationship between the magnitude of the speed of sound and the QCD phase structure is discussed, and the regions where the acoustic equation fails are indicated under different physical conditions. It is found that the boundary of vanishing sound speed in asymmetric quark matter is smaller than that in symmetric quark matter, meaning that the range where the acoustic wave equation fails in asymmetric quark matter is smaller than that in symmetric quark matter. The results also indicate that in most of the stable phase, the speed of sound in asymmetric quark matter is slightly larger than that in symmetric quark matter.