Plane waves Definition and 61 Threads

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






x
→





{\displaystyle {\vec {x}}}
in space and any time



t


{\displaystyle t}
, the value of such a field can be written as




F
(



x
→



,
t
)
=
G
(



x
→



⋅



n
→



,
t
)
,


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






n
→





{\displaystyle {\vec {n}}}
is a unit-length vector, and



G
(
d
,
t
)


{\displaystyle G(d,t)}
is a function that gives the field's value as from only two real parameters: the time



t


{\displaystyle t}
, and the displacement



d
=



x
→



⋅



n
→





{\displaystyle d={\vec {x}}\cdot {\vec {n}}}
of the point






x
→





{\displaystyle {\vec {x}}}
along the direction






n
→





{\displaystyle {\vec {n}}}
. The latter is constant over each plane perpendicular to






n
→





{\displaystyle {\vec {n}}}
.
The values of the field



F


{\displaystyle F}
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


{\displaystyle F}
are vectors, the wave is said to be a longitudinal wave if the vectors are always collinear with the vector






n
→





{\displaystyle {\vec {n}}}
, and a transverse wave if they are always orthogonal (perpendicular) to it.

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