To find the maximum amplitude in a superposition of waves, you need to consider the principle of superposition, which states that when two or more waves overlap, the resulting displacement at any point is the algebraic sum of the individual displacements of the waves.
When waves superpose, their individual amplitudes add together. If you have two waves with amplitudes A1 and A2, the resulting maximum amplitude A_max can be found by adding the individual amplitudes:
A_max = A1 + A2
If you have more than two waves superposing, you simply continue adding the individual amplitudes to obtain the maximum amplitude of the superposition.
It's important to note that this assumes the waves are in phase at the point of superposition. If the waves have different phases or are not in phase, the resulting amplitude may vary, and additional considerations such as interference effects may come into play.