Question

Will plane waves incident upon a small opening in a barrier fan out on the other side or continue as plane waves?

Answer 1

Plane waves incident upon a small opening in a barrier will fan out and decrease in amplitude.

In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space.

For any position vector x in space and any time t, the value of such a field can be written as :

${\displaystyle F({\vec {x}},t)=G({\vec {x}}\cdot {\vec {n}},t),}$

${\displaystyle F({\vec {x}},t)=G({\vec {x}}\cdot {\vec {n}},t),}{\displaystyle F({\vec {x}},t)=G({\vec {x}}\cdot {\vec {n}},t),}$

where ${\displaystyle {\vec {n}}}\vec$ is a unit-length vector, and ${\displaystyle G(d,t)}{\displaystyle G(d,t)}$  is a function that gives the field's value as dependent on only two real parameters: the time t, and the scalar-valued displacement

${\displaystyle d={\vec {x}}\cdot {\vec {n}}}{\displaystyle d={\vec {x}}\cdot {\vec {n}}}$

of the point ${\displaystyle {\vec {x}}}{\vec {x}}$ along the direction ${\displaystyle {\vec {n}}}\vec$. The displacement is constant over each plane perpendicular to ${\displaystyle {\vec {n}}}\vec$.

The values of the field may be scalars, vectors, or any other physical or mathematical quantity. They can be complex numbers, as in a complex exponential plane wave.

When the values of F are vectors, the wave is said to be a longitudinal wave if the vectors are always collinear with the vector ${\displaystyle {\vec {n}}}\vec$, and a transverse wave if they are always orthogonal (perpendicular) to it.

Learn more about Plane waves here : brainly.com/question/15414918

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