General Form
In general, the function may also have:
- a spatial dimension, x (aka position), with wavenumber k
- a non-zero center amplitude, D
which looks like this:
The wavenumber is related to the angular frequency by:.
where λ is the wavelength, f is the frequency, and c is the speed of propagation.
This equation gives a sine wave for a single dimension, thus the generalized equation given above gives the amplitude of the wave at a position x at time t along a single line. This could, for example, be considered the value of a wave along a wire.
In two or three spatial dimensions, the same equation describes a travelling plane wave if position x and wavenumber k are interpreted as vectors, and their product as a dot product. For more complex waves such as the height of a water wave in a pond after a stone has been dropped in, more complex equations are needed.
Read more about this topic: Sine Wave
Famous quotes containing the words general and/or form:
“The most general deficiency in our sort of culture and education is gradually dawning on me: no one learns, no one strives towards, no one teaches—enduring loneliness.”
—Friedrich Nietzsche (1844–1900)
“The old idea that the joke was not good enough for the company has been superseded by the new aristocratic idea that the company was not worthy of the joke. They have introduced an almost insane individualism into that one form of intercourse which is specially and uproariously communal. They have made even levities into secrets. They have made laughter lonelier than tears.”
—Gilbert Keith Chesterton (1874–1936)