- #1

- 54

- 0

## Main Question or Discussion Point

Is there a physical unit related to the Green's function of the wave equation?

In particular, let

[tex]\nabla^2 P -\frac{1}{c^2}\frac{\partial^2 P}{\partial t^2} = f(t)[/tex]

where P is pressure in Pa. Since the Green's function solves the PDE when f(t) is the delta function, the Green's function G has a unit of Pa.

The solution to the inhomogeneous PDE is

P = G*f(t),

where * denotes convolution. This leads to contradiction since LHS is in Pa and RHS is in Pa * Pa/m^2 * (sec m^3), where (Pa/m^2) is the unit of f(t) and (sec m^3) denotes the integration in both space and time.

Thx.

In particular, let

[tex]\nabla^2 P -\frac{1}{c^2}\frac{\partial^2 P}{\partial t^2} = f(t)[/tex]

where P is pressure in Pa. Since the Green's function solves the PDE when f(t) is the delta function, the Green's function G has a unit of Pa.

The solution to the inhomogeneous PDE is

P = G*f(t),

where * denotes convolution. This leads to contradiction since LHS is in Pa and RHS is in Pa * Pa/m^2 * (sec m^3), where (Pa/m^2) is the unit of f(t) and (sec m^3) denotes the integration in both space and time.

Thx.