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Spatial and temporal periods and periodic functions 
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#1
Apr1914, 08:18 PM

P: 686

A periodic function is one that ##f(\theta) = f(\theta + nT)##, by definition. However, the argument ##\theta## can be function of space and time ( ##\theta(x, t)## ), so exist 2 lines of development, one spatial and other temporal: $$f(\theta) = f(kx + \varphi) = f(2 \pi \xi x + \varphi) = f\left(\frac{2 \pi x}{\lambda} + \varphi \right)$$ $$f(\theta) = f(\omega t + \varphi) = f(2 \pi \nu t + \varphi) = f\left(\frac{2 \pi t}{T} + \varphi \right)$$ or the both together: $$f(\theta) = f(kx + \omega t + \varphi) = f(2 \pi \xi x + 2 \pi \nu t + \varphi) = f\left(\frac{2 \pi x}{\lambda} + \frac{2 \pi t}{T} + \varphi \right)$$ so, becomes obvius that ##\lambda## is the analogus of ##T##, thus the correct wound't be say that a periodic function is one that ##f(\theta) = f(\theta + nT + m\lambda)## ?



#2
Apr1914, 09:38 PM

P: 423




#3
Apr2014, 03:24 PM

P: 686

happens that when I ploted in the geogebra the wave ##f(\theta(x,t)) = \cos(kx  wt)## happend that ##f(\theta) = f(\theta + m \lambda)## but ##f(\theta) \neq f(\theta + n T)## Why???



#4
Apr2014, 08:33 PM

P: 423

Spatial and temporal periods and periodic functions



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