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 animation onde stationnaire p1+p2

acoustics animation page

You can use images and animations included in this page for teaching using, but please acknowledge where you obtained the animation!
here: Catherine Potel and Michel Bruneau (Université du Maine - France)

See the slides associated to chapter 4 of the fluid acoustic course   
General definition: a stationary (standing) wave is a wave for which the associated REAL physical quantity (acoustic pressure, particle velocity, potential) can be written in the form of the product of a function depending on the spatial variables x, y, z, and of a function depending on the time t:
p(x,y,z;t) = P(x,y,z) T(t).
Generally speaking, P(x,y,z) is not necessarily a sinusoidal function, whereas T(t) is necessarily a sinusoidal function. On the other hand, if P(x,y,z) can be written as P(x,y,z) = P1(x) P2(y,z), then P1(x) is necessarily a sinusoidal function, whereas P2(y,z) is not necessarily a sinusoidal function.

Particular case of a unidimensional problem

Here, X(x) is necessarily a sinusoidal function (see opposite figure).

animation onde aller p1
Direct wave p1propagative wave in the direction x>0
animation onde retour p2
Return wave p2 : propagative wave in the direction x<0
animation onde stationnaire p1+p2
Stationary wave p1+p2: the spatial position of the antinodes (maxima or minima) and of the nodes (zeroes) of the acoustic pressure does not change, but their amplitude varies with time.