Macagno formula

Macagno formula is analytic estimate of coefficient of reflection of monochromatic wave at the surface of a liquid from a П–shaped inhomogeniety.

The reflection coefficient \(R\) is approximated with expression

\(\displaystyle R= \left( 1+ \left( kw \frac{ \sinh(kh) }{ 2 \cosh(kh\!-\!kd) }\right)^2 \right)^{-1/2}\)

where \(k\) is wavenumber,

\(h\) is water depth

\(w\) is width of the obstacle

\(d\) is draft (height) of the obstacle.

Using dimensions variables \(H=kh\), \(W=kw\), \(d=kD\),

the estimate can be written as follows:

\(\displaystyle R= \left( 1+ \left( W \frac{ \sinh(H) }{ 2 \cosh(H\!-\!D) }\right)^2 \right)^{-1/2}\)

The formula looks strange, as it predicts reduction of the reflection coefficient to zero at large values of \(W\).

Keywords
Zeno effect