Question

(a) Find the Fourier transform of the following function

(b) Using Fourier transforms, solve the wave equation

, -∞<x<∞ t>0

and bounded as $x \rightarrow \pm$ ∞

f(r)e u(r, 0)e 4(r.0) =0 , t ur.

Answer 1

X he ajintem Trans foom , wu heue Forunier the fcn dr Ff e e C iSx- af S+x e. C -is)x +is)x e a a haue e We - 1-s) +is)x e - hane tale O O 1+S 1-2S -S 1+ -2S

(is) (-s) 2 2 2 |지 2 st