Representation of Waves Using Exponentials

It is convenient to represent waves using exponential functions. For example a stationary wave can be described by the function: = Ae,
where the constant A is a real number. The function can be resolved into its real and imaginary parts using Euler's equation,
::e = cos + isin,
to obtain
:: = Acos(kx) + iAsin(kx).
A travelling stationary wave can be described by exponential function
::,(t) = Ae
The exponential function has mathematical properties, which makes it more convenient to use than trigonometric functions. For instance the product of an exponential function e and a second exponential function e can be evaluated by simply adding the exponents:
::ee = e
Category:Physics