Coherent waves are waves that have a constant phase difference between them. This means that the peaks and troughs of the waves occur at the same time and at the same position. There are several factors that determine the coherence of waves, including frequency, phase difference constant, amplitude, and wavelength in phase with each other. However, the factor that is not the same for coherent waves is the amplitude.

Amplitude refers to the maximum displacement or distance the wave moves from its equilibrium position. It is a measure of the energy carried by the wave. In the case of coherent waves, the amplitudes may be different for each wave. This means that one wave may have a larger maximum displacement compared to another wave. Despite the difference in amplitude, as long as the waves have a constant phase difference, they can still be considered coherent.

The other factors, on the other hand, are the same for coherent waves. Let's discuss them in further detail:

1. Frequency: Frequency refers to the number of complete oscillations or cycles of a wave that occur in one second. In the case of coherent waves, the frequencies are the same. This means that the waves complete the same number of cycles in the same amount of time.

2. Phase Difference Constant: Phase difference refers to the difference in phase between two waves at a given point in time. In the case of coherent waves, the phase difference remains constant. This means that the waves maintain a consistent phase relationship throughout their propagation.

3. Wavelength in Phase with Each Other: Wavelength refers to the distance between two consecutive points that are in phase with each other. In the case of coherent waves, the wavelengths are the same. This means that the waves have the same distance between two corresponding points, such as two peaks or two troughs.

In summary, while frequency, phase difference constant, and wavelength in phase with each other are the same for coherent waves, the amplitude can differ between the waves. This means that coherent waves can have different maximum displacements or energy levels, but they still maintain a constant phase relationship.