There is yet another way to find the general solution to the wave equation which is valid in 1, 2, or 3 (or more!) dimensions. This method is quite important and, as we shall see, can often be used for other linear homogeneous differential equations. This technique for solving the wave equation is called the method of separation of variables.
separation of variable, superposition, wave, chapter 11
Torre, Charles G., "11 Separation of Variables" (2012). Foundations of Wave Phenomena. Book 12.