This report gives a discussion of a new wave characteristic as a material parameter for a composite with the magnetoelectric effect. The new parameter depends on the material constants of a piezoelectromagnetic composite. It can be implemented on : (A) mechanically free, electrically and magnetically open surface and (B) mechanically free, electrically and magnetically closed surface. These theoretical investigations are useful for researches in the firlds of acousto-optics, photonics and opto-acousto-electronics. Some sample calculations are carried out for BaTiO₃ - CoFe₂O₄ and PZT-5H-Terfenol-D composites of class $6 mm$. Also, the first and second derivatives of the new parameter with respect to the electromagnetic constant 𝛼 are graphically shown.