(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The temporal average of a function f(t) over an interval T is given by [tex]\langle f(t) \rangle=\frac{1}{T} \int _{t}^{t+T} f(t') dt'[/tex].

Let [tex]\tau =\frac{2 \pi}{\omega}[/tex]. Calulate the temporal average of [tex]\langle \sin ^2 (\vec k \cdot \vec r - \omega t) \rangle =\frac{1}{2}[/tex], when [tex]T=\tau[/tex] and [tex]T >> \tau[/tex].

2. Relevant equations

Already given in the problem description.

3. The attempt at a solution

I don't understand the problem. Aren't they asking me to prove that [tex]\langle \sin ^2 (\vec k \cdot \vec r - \omega t) \rangle =\frac{1}{2}[/tex] for [tex]T=\tau[/tex] and to calculate [tex]\langle \sin ^2 (\vec k \cdot \vec r - \omega t) \rangle[/tex] for [tex]T>> \tau[/tex]? If so, it's really not clear. If not, could you please explain with a bit more details? I can't start the problem since I don't understand it.

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# Temporal average

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