Yes, two waves can have different amplitudes and the same frequency but different phase differences. In fact, this is quite common in wave phenomena. Let's consider two waves:
Wave 1: A1 * sin(ωt + φ1) Wave 2: A2 * sin(ωt + φ2)
In these equations, A1 and A2 represent the amplitudes of the waves, ω represents the angular frequency (which is related to the frequency by ω = 2πf), t represents time, and φ1 and φ2 represent the phase differences of the waves.
If the frequencies of the two waves are the same, they will oscillate with the same number of cycles per unit of time. However, the amplitudes A1 and A2 can be different, indicating different strengths or intensities of the waves.
The phase differences φ1 and φ2 determine the relative positions of the waves at a given time. If φ1 and φ2 are different, the waves will have different initial positions in their cycles. This difference in phase can lead to various interference effects when the waves are combined or superimposed.
It's important to note that the resulting combined wave will depend on the specific values of the amplitudes and phase differences of the two waves. The superposition of waves with different amplitudes and phase differences can result in constructive interference (where the amplitudes add up) or destructive interference (where the amplitudes partially or completely cancel each other out), leading to a variety of resulting waveforms.