When two coherent waves (waves with a constant phase difference) converge or overlap, their effects depend on the relative phases of the waves at each point where they meet. This phenomenon is known as interference.

1. Constructive Interference: Constructive interference occurs when the crests of one wave align with the crests of the other wave, and the troughs align with troughs. As a result, the amplitudes of the waves add together, reinforcing each other. This reinforcement leads to a wave with a greater amplitude than either of the individual waves. In mathematical terms, for waves of equal amplitude, constructive interference occurs when the phase difference between the waves is an integer multiple of the wavelength (�⋅�m⋅λ), where �m is an integer.

2. Destructive Interference: Destructive interference occurs when the crests of one wave align with the troughs of the other wave. In this case, the positive amplitudes of one wave cancel out the negative amplitudes of the other wave. As a result, the waves partially or completely cancel each other out at certain points, leading to a reduction or even elimination of the overall amplitude. In mathematical terms, for waves of equal amplitude, destructive interference occurs when the phase difference between the waves is an odd integer multiple of half the wavelength ((2�+1)⋅�2(2m+1)⋅2λ​), where �m is an integer.