At one point and instant, two waves give displacements \(y_1=2.0\,\mathrm{mm}\) and \(y_2=-0.5\,\mathrm{mm}\). Find the resultant displacement.

Two equal sinusoidal waves of amplitude \(A\) are exactly in phase. What is the resultant amplitude?

Two equal sinusoidal waves of amplitude \(A\) differ in phase by \(\pi\). What is the resultant amplitude?

Two equal sinusoidal waves each have amplitude \(4.0\,\mathrm{mm}\) and phase difference \(60^\circ\). Find the resultant amplitude.

Explain why interference is described by adding displacements rather than by adding energies directly.

Two equal waves produce a resultant amplitude of \(A\). Find the phase difference between them.

Two equal waves each have amplitude \(A\). For what phase difference does the resultant amplitude become \(\sqrt{3}\,A\)?

Two equal sinusoidal waves overlap. Find all phase differences in the range \(0\le \Delta\phi\le \pi\) for which the resultant amplitude is at least \(1.5A\).