Abstract For gradient-based acoustical topology optimization, the acoustical properties of an acoustic medium are interpolated. Although the lower limit values of the density and sound speed simulating a rigid body affect the accuracy of the final results significantly, an in-depth study on the selection of these limit values is rare. In the first part of this work, the importance of the proper choice of the limit values was demonstrated with an example to show that improperly-selected limit values can result in erroneous eigenvalues and eigenmodes of an optimized acoustic cavity. Then, by using two theoretical models representing typical air-rigid body configurations, the effects of the density and sound speed values of a simulated rigid body were investigated by the power transmission coefficient. From the findings of the theoretical investigation, a guideline for properly selecting the low limit values of the density and sound speed of a simulated rigid body is suggested. The validity of the guideline will be checked in numerical case studies.