No, coherence does not necessarily imply that all waves are the same. Coherence refers to the degree of similarity or correlation between two or more waves. It describes the relationship between the phases of different waves.
In the context of waves, coherence can be classified into two main types: spatial coherence and temporal coherence.
Spatial coherence: Spatial coherence refers to the correlation of wave phases at different points in space. If waves at different locations have a consistent phase relationship, they are considered spatially coherent. For example, if you have two water waves propagating in a pond and their crests and troughs align consistently as they travel, they can be said to be spatially coherent.
Temporal coherence: Temporal coherence refers to the correlation of wave phases at different points in time. If waves at different instances of time exhibit a consistent phase relationship, they are considered temporally coherent. For example, if you have two waves of the same frequency and their wave crests and troughs align consistently over time, they can be considered temporally coherent.
So, coherence is a measure of the similarity of wave phases between different points in space or time. However, it does not necessarily mean that all waves are the same. Waves can have different amplitudes, frequencies, and shapes, even if they are coherent. Coherence simply describes the correlation of the phases of different waves.