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:
“There are two great rules in life, the one general and the other particular. The first is that every one can in the end get what he wants if he only tries. This is the general rule. The particular rule is that every individual is more or less of an exception to the general rule.”
—Samuel Butler (1835–1902)
“I am afraid I am one of those people who continues to read in the hope of sometime discovering in a book a single—and singular—piece of wisdom so penetrating, so soul stirring, so utterly applicable to my own life as to make all the bad books I have read seem well worth the countless hours spent on them. My guess is that this wisdom, if it ever arrives, will do so in the form of a generalization.”
—Joseph Epstein (b. 1937)