Simple Source Formulation [Williams]

Interior Problem (n points inward)

∂V

S(x0

, ω)

∂G(x|x0

, ω)

∂(n, x0

)

− G(x|x0

, ω)

∂S(x, ω)

∂(n, x)

x=x0

dS0

=

S(x, ω) x ∈ V

1

2

S(x, ω) x ∈ ∂V

0 x ∈ ¯

V

Exterior Problem (n points inward)

∂V

Psc

(x0

, ω)

∂G(x|x0

, ω)

∂(n, x0

)

− G(x|x0

, ω)

∂Psc

(x, ω)

∂(n, x)

x=x0

dS0

=

0 x ∈ V

−1

2

Psc

(x, ω) x ∈ ∂V

−Psc

x ∈ ¯

V

(Interior)+(Exterior) together with S(x, ω) + Psc

(x, ω) = 0 for x ∈ ∂V

−

∂V

G(x|x0

, ω)

∂(S(x, ω) + Psc

(x, ω)

∂(n, x)

x=x0

dS0

=

S(x, ω) x ∈ V

S(x, ω) x ∈ ∂V

−Psc

(x, ω) x ∈ ¯

V

Spors, Zotter | Sound Field Synthesis | Conclusions 26