When we were solving the wave equations in the case of $2$ different mediums, we were assuming that, when a longitudinal wave reaches the border, there will be 1 reflected longitudinal and 1 reflected transversal, and there will also be 1-1 transent wave. But, in the case of the initial wave is transversal, we were assuming only transversal waves. Why did we do it this way?
The equation is: $$\frac{\partial^2 \vec{u}}{\partial t^2}=c^2 \bigtriangleup \vec{u}$$