General Relation for Field Admittance and Intensity

→ See also Mechel, Vol. I, Ch. 3 (1989)

The vector component G${}_{{n}}$ in a direction n of the field admittance G

is defined by $\displaystyle G_{n}=\frac{v_{n}}{p}=\frac{j}{k_{0}Z_{0}}\;\frac{\partial p/\partial n}{p}$. (1)

If the sound pressure is described by

magnitude and phase $\displaystyle p(r)=\;|p(r)|\cdot e^{{j\,\varphi(r)}}$, (2)

the field admittance is given by $\displaystyle G_{n}(r)=\frac{1}{k_{0}Z_{0}}\left[{-\frac{\partial}{\partial n}\varphi(r)+j\cdot\frac{\partial}{\partial n}\ln\,\left({|p(r)|}\right)}\right]$. (3)

Near an absorbing wall the reactance of the wall admittance determines the slope of sound pressure level by the term ln($|$p(r)$|)$ (“admittance rule”).

The time-averaged intensity

of a harmonic wave is$\displaystyle I_{n}=\displaystyle\frac{1}{2}\; p\cdot v_{n}^{\ast}=\displaystyle\frac{1}{2}\; G_{n}^{\ast}\cdot|p|^{2}$. (4)

With the admittance relation

follows: \(\displaystyle I_{n}=-\frac{|p(r)|^{2}}{2\,...