This publication contains a mathematical approach for a reinterpretation of the electromagnetic wave equation given a magnetic and electric field density. The basis for this is the essay"The Reinterpretation of the 'Maxwell Equations'" (Martin, 2021). In this paper it is shownthat there is a magnetic field density due to the fact that div u20d7B is equal to (Sp)grad Bu20d7 .The same approach applies to the electric field density. The consequence of this is that boththe magnetic field density and the electric field density not only play an important role in the"Maxwell equations", but also in the calculation of the electromagnetic wave equation.In this publication, the electromagnetic wave equation is calculated with the help of vectorcalculus. First, the individual components of the magnetic wave and the individual components of the electric wave are derived.Furthermore, it is shown that the individual components of the two types of waves result inthree different directions of movement, which the respective field can theoretically achieve inthe direction of propagation. In addition, the Poynting vector shows a longitudinal energywave in the direction of propagation of the electromagnetic wave, which is suitable for energy transport.As already mentioned, the calculations made in this elaboration are based on the principles ofvector calculation and show a transverse wave component, a longitudinal and a combinedwave component of the electromagnetic wave.