One example where two waves can have equal amplitudes but different phases is in the case of two simple harmonic waves or sinusoidal waves. Let's consider two waves with the same amplitude, A, but different phases, represented by the equations:
Wave 1: y₁ = Asin(ωt) Wave 2: y₂ = Asin(ωt + φ)
In these equations, y₁ represents the displacement of particles in wave 1, y₂ represents the displacement of particles in wave 2, ω represents the angular frequency, t represents time, and φ represents the phase difference between the two waves.
Both waves have the same amplitude, A, which determines the maximum displacement of particles from their equilibrium positions. However, the phase difference φ determines the relative position or starting point of the waves in their oscillatory motion.
For example, if wave 1 is at its maximum amplitude when wave 2 is at its minimum amplitude, they would be out of phase by half a cycle or have a phase difference of φ = π radians. In this case, the two waves would have equal amplitudes but different phases.
This scenario can be visualized by considering two points on a rotating wheel. If the points start at different positions on the wheel, they will have different phases, even if they both have the same maximum distance from the center (amplitude).