When a crest and a trough of different amplitudes overlap, it results in a type of interference called "partial destructive interference" or "partial cancellation."
Interference occurs when two or more waves meet and combine their amplitudes. Depending on their relative phase and amplitude, the resulting interference can be constructive or destructive.
In the case you described, when a crest and a trough of different amplitudes overlap, the amplitudes of the two waves partially cancel each other out. The resultant wave will have a smaller amplitude than either of the individual waves.
The degree of cancellation depends on the difference in amplitudes between the crest and trough. If the amplitudes are similar, the cancellation will be more significant. However, if the difference in amplitudes is small, the cancellation will be less pronounced.
It's worth noting that the interference pattern resulting from the overlap of waves is complex and can vary depending on the specific amplitudes, wavelengths, and phases involved. In some cases, the resulting wave may still exhibit some degree of constructive interference or interference patterns with varying amplitudes along the wave. The exact characteristics of the interference pattern would require a more detailed analysis of the specific wave properties.