If the phase difference between the two wave is `2 pi` during superposition, then the resultant amplitude is

Options

A. maximum
B. minimum
C. maximum or minimum
D. none of the above

Answer

To solve the problem of finding the resultant amplitude when the phase difference between two waves is \(2\pi\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amplitudes**:
Let the amplitudes of the two waves be \(A_1\) and \(A_2\).

2. **Use the Resultant Amplitude Formula**:
The formula for the resultant amplitude \(R\) when two waves interfere is given by:
\[ R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cos(\phi)} \]
where \(\phi\) is the phase difference between the two waves.

3. **Substitute the Phase Difference**:
According to the problem, the phase difference \(\phi\) is \(2\pi\). We substitute this value into the formula:
\[ R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cos(2\pi)} \]

4. **Calculate \(\cos(2\pi)\)**:
We know that \(\cos(2\pi) = 1\). Therefore, we can simplify the equation:
\[ R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2 \cdot 1} \]

5. **Simplify Further**:
This simplifies to:
\[ R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2} = \sqrt{(A_1 + A_2)^2} \]

6. **Final Result**:
Taking the square root gives us:
\[ R = A_1 + A_2 \]
Thus, the resultant amplitude when the phase difference is \(2\pi\) is simply the sum of the two amplitudes.

### Conclusion:
When the phase difference between two waves is \(2\pi\), the resultant amplitude is \(A_1 + A_2\).