A two dimensional rectangular slab (with the two sides of length a and b) has its edges fixed; at time \(t = 0\) it has the profile
\[ u ( x , y , 0 ) = \sin \frac { 2 x \pi } { a } \sin \frac { 3 y \pi } { b } ;\tag{41} \]
find \(u ( x , y , t )\) knowing that it satisfies the wave equation with a velocity v.