Question

is it necessary to master transverse and longitudinal waves before studying the wave theory of light???

Answer 1

Yes, transverse waves at least. You need to be able to understand what stuff like
\[x(t) = Asin(\omega t)\]
and
\[\Psi(x, t) = Acos(kx - \omega t)\]
mean, and be able to manipulate them easily. I suppose you could get a decent understanding without it, but knowing the calculus/diff eq behind it is just about necessary.