No, two waves do not have to have the same amplitude in order to have a wave front. The concept of a wave front refers to a continuous surface or plane that connects points on a wave that are in the same phase. It is independent of the amplitude of the wave.
In a wave, the wave front represents the region of the wave that has traveled the same distance from the source at the same time. It can be visualized as a line or surface that is perpendicular to the direction of wave propagation and connects points of the wave that are in phase.
When two waves with different amplitudes interact, the resulting wave front will depend on the specific characteristics and interference patterns of those waves. The amplitude of a wave affects the intensity or energy of the wave, but it does not determine the shape or structure of the wave front.
If two waves with different amplitudes interfere constructively (i.e., their crests align with each other), the resulting wave front may exhibit a larger amplitude at those points of constructive interference. However, the overall shape and nature of the wave front will still be determined by the relative phases and positions of the individual waves.
On the other hand, if the waves interfere destructively (i.e., their crests align with troughs), the resulting wave front may exhibit regions with reduced or even zero amplitude. Again, the wave front will primarily depend on the phase relationships and positions of the interacting waves, regardless of their amplitudes.
In summary, the presence or nature of a wave front is not determined by the similarity or difference in amplitudes between two waves. The wave front represents the connectivity of points in the wave that are in phase, and it is determined by the relative phases and positions of the individual waves.