## Time Average

• The time average of a function is found by evaluating the integral:

with the average taken over a time, ΔT.

Time averages are often important when considering oscillating waves of the form:

where ω is the angular frequency and A is the amplitude. The instantaneous value of this wave varies between -A and A, however, the time average of this wave over one period is .

Another common example (such is in the calculation of the intensity of an electromagnetic wave) is to find the time average of the functions

 and

Using the equation (1) above, it can be shown that:

.