In this article, first we present a new approach based on Green's formula, to describe the uniqueness and existence of the solution of the Helmholtz equation. By imposing at infinity the outgoing wave condition or also called Sommerfeld radiation condition, we show how it is possible to define in a natural way an outgoing solution of the Helmholtz equation based on physical arguments. Then, we resolve the exterior problem, given by the scattering of time-harmonic acoustic wave by sound-soft obstacle, which leads to find a radiating solution to the Helmholtz equation
