When two waves overlap, the outcome is determined by the principle of superposition. According to this principle, the resultant wave amplitude at any given point is the sum of the amplitudes of the individual waves at that point.
Here's a detailed explanation of the process:
1. Identify the Amplitudes of the Waves:
- If we denote the amplitude of the first wave as [tex]\(A_1\)[/tex] and the amplitude of the second wave as [tex]\(A_2\)[/tex], we need to know these values to compute the resultant amplitude.
2. Determine the Phases of the Waves:
- If the waves overlap in phase (i.e., the crest of one wave aligns with the crest of the other), the amplitudes will add together constructively.
- If the waves overlap out of phase (i.e., the crest of one wave aligns with the trough of the other), the amplitudes will subtract destructively.
3. Calculate the Resultant Amplitudes:
- If the waves are in-phase, the total amplitude [tex]\(A_{total}\)[/tex] will be [tex]\(A_{total} = A_1 + A_2\)[/tex].
- If the waves are out-of-phase, the total amplitude [tex]\(A_{total}\)[/tex] will be [tex]\(A_{total} = A_1 - A_2\)[/tex].
Since the problem does not provide specific amplitudes for the waves, we cannot calculate an exact numerical result. However, the key concept is that the resultant amplitude at the moment the waves overlap is the sum of the amplitudes of each wave, considering their phase relationship.
In Summary:
The solution to determining the outcome when these two waves overlap depends on the provided amplitudes of the waves and their respective phases at the point of overlap. You sum the amplitudes of the waves based on whether they are in-phase (constructive interference) or out-of-phase (destructive interference).
