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.

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

Direct wave p1 :  propagative wave in the direction x>0	Return wave p2 : propagative wave in the direction x<0
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.