This is a generally true statement for any standing wave. But let's think about standing waves conceptually, before we lay out the mathematics behind their amplitude.
Consider that a standing wave exists along some length x, from 0 to L. For a particular type of standing wave, we establish that at x = 0 a node exists, and likewise at x = L. Recall that a node in a standing wave is the location in x where no oscillations occur. Alternately, an antinode is the location where maximum oscillation occurs. (As a property) all antinodes lie exactly between the two closest nodes, so we know that at least one antinode exists between our two nodes, x = 0 and x = L. We can place no nodes between 0 and L, in which case the antinode is at location x = L/2. Or we can place one node between 0 and L, in which case the node is at location x = L/2. Notice this divides the wave into 2 equal parts. Placing 2 nodes ensures that they be placed at x1 = L/3 and x2 = 2*L/3, dividing the wave into 3 equal regions. Generally if you place n new nodes, you divide the standing wave into (n+1) regions. When you do so, you fix the wavelength of the standing wave, as λ = 2*L/(n+1). You can derive the wavelength by finding the length between adjacent nodes, and doubling it.
This type of standing wave can be modeled with the function:
U(x,t) = A*sin(2πx/λ)*sin(ωt), where A is the constant maximum amplitude of the standing wave (Recall: this happens at the antinodes). Alternately we can write:
U(x,t) = A*sin((πx)*(n+1) / L)*sin(ωt)
We know that sin( multiple of π) = 0, so we can check that this equation gets nodes where we expect them. In any case, we know that any point in x will oscillate up and down, with frequency ω, unless it is a node. So any point between nodes will oscillate, but with what amplitude? The amplitude of a particular point will be what is left from the equation, namely [A*sin((πx)*(n+1) / L)]. Notice this is = 0 if x is a node and equal to A if x is an antinode. So generally any point between a successive node and antinode must vary in amplitude, sinusoidally.
Hope this helps you understand.
