Difference between revisions of "Template:Incident potential for two dimensions"
| Line 1: | Line 1: | ||
===Incident potential=== | ===Incident potential=== | ||
| − | To create meaningful solutions of the velocity potential <math>\phi</math> in the specified domains we add an incident wave term to the expansion for the domain of <math>x < 0</math>. The incident potential is a wave of amplitude <math>A</math> | + | To create meaningful solutions of the velocity potential <math>\phi</math> in the specified domains we add an incident wave term to the expansion for the domain of <math>x < 0</math> above. The incident potential is a wave of amplitude <math>A</math> |
in displacement travelling in the positive <math>x</math>-direction. We would only see this in the time domain <math>\Phi(x,z,t)</math> however, in the frequency domain the incident potential can therefore be written as | in displacement travelling in the positive <math>x</math>-direction. We would only see this in the time domain <math>\Phi(x,z,t)</math> however, in the frequency domain the incident potential can therefore be written as | ||
<center> | <center> | ||
Revision as of 05:30, 6 March 2012
Incident potential
To create meaningful solutions of the velocity potential [math]\displaystyle{ \phi }[/math] in the specified domains we add an incident wave term to the expansion for the domain of [math]\displaystyle{ x \lt 0 }[/math] above. The incident potential is a wave of amplitude [math]\displaystyle{ A }[/math] in displacement travelling in the positive [math]\displaystyle{ x }[/math]-direction. We would only see this in the time domain [math]\displaystyle{ \Phi(x,z,t) }[/math] however, in the frequency domain the incident potential can therefore be written as
[math]\displaystyle{ \phi^{\mathrm{I}}(x,z) =e^{-k_{0}x}\chi_{0}\left( z\right). }[/math]
The first term in the expansion of the diffracted potential for the domain [math]\displaystyle{ x \lt 0 }[/math] is given by
[math]\displaystyle{ a_{0}e^{k_{0}x}\chi_{0}\left( z\right) }[/math]
which represents the reflected wave.
