Formation by the graphical method
Draw the two opposite-travelling waves at t = 0, T/8, T/4, 3T/8, T/2 and add them point by point. At t = 0 and t = T/2 the components coincide and the resultant has twice the amplitude; at t = T/4 and 3T/4 the components are exactly antiphase everywhere and the resultant is zero at every position. The positions of the zeros never move, and these fixed zeros are the nodes.
What this actually means
The method is mechanical: shift one wave a distance λ/8 to the right and the other λ/8 to the left for each T/8 step, then add ordinates. Do not try to guess the resultant.
The moment everyone misreads is t = T/4. The whole string is flat, so students conclude the stationary wave has vanished. It has not. Every particle is passing through equilibrium at maximum speed, and a moment later the pattern reappears inverted.
The give-away that this is stationary and not progressive is that the zero crossings sit at the same x for every frame. In a progressive wave the zeros march along.
When you sketch the finished stationary wave, draw the two extreme profiles (solid and dashed) forming the envelope, and mark N and A on the axis. Markers want the envelope, not one snapshot.
Take the wavelength from the component waves, not from the envelope. Each loop of the envelope is only half a wavelength wide.
Concluding the stationary wave has disappeared at the flat instant, instead of saying every particle is momentarily at zero displacement but moving at maximum speed.
Prove it — watch it be true
- Use the time snap buttons to step through t = 0, T/8, T/4, 3T/8, T/2.
- At t = T/4 confirm the resultant trace is completely flat while the two components are still drawn and still moving.
- Step back to t = 0 and confirm the same zero positions are unchanged in every frame.