1. General solution of the wave equation using Fourier Transforms. Define the

Fourier Transform pair as (note the sign difference in the definition from that of

Haberman, § 10.3.2)

ƒ(k) =

f(x)e ikzdr f(x)

(a) Show that the general solution of (§ 10.6.1 of Haberman)

Pu

Ət²

f(x),

is

1

ikr

2/7 f(k) e³kx dk,

2π

2 Pu

əx²

u(x,0)

(-∞0

Ju(x, 0)

Ət

u(x,t) = ½ [ƒ(x − ct) + f(x + ct)]

0

(1)

(2)

(3)