Introduction:
When two waves interfere, their amplitudes can add up constructively or destructively. Complete destructive interference occurs when the waves are perfectly out of phase and cancel each other out completely at a specific point. In this case, the phase difference between the waves is zero.

Explanation:
To determine the condition for complete destructive interference at point P, we need to consider the phase difference between the waves originating from sources S1 and S2. Let's denote the distance between source S1 and point P as S1P and the distance between source S2 and point P as S2P.

Phase Difference:
The phase difference between two waves is given by the equation:

Phase difference (Δϕ) = (2π/λ) * Δx

Where λ is the wavelength of the waves and Δx is the difference in distances between the sources and the point of interest.

Condition for Destructive Interference:
For complete destructive interference, the phase difference between the waves should be an odd multiple of π (180 degrees). Mathematically, this can be expressed as:

Δϕ = (2n + 1) * π

Where n is an integer.

Applying the Condition:
Let's consider the distance between the sources S1 and S2 as d. Since the phase difference is zero, we can set up the equation as:

(2π/λ) * (S1P - S2P) = 0

Simplifying the equation, we get:

S1P - S2P = 0

Therefore, the difference in distances between the sources and point P should be equal for complete destructive interference.

Conclusion:
In conclusion, for two waves originating from sources S1 and S2 to show complete destructive interference at point P, the difference in distances between the sources and point P should be zero. This means that the waves should travel equal distances from their respective sources to point P.