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

Answer

To find the resultant amplitude when the phase difference between two waves is \(2\pi\) radians, we can follow these steps:

### Step 1: Understand the Formula for Resultant Amplitude
The resultant amplitude \(R\) when two waves interfere can be calculated using the formula:
\[ R = \sqrt{a_1^2 + a_2^2 + 2a_1a_2 \cos \phi} \]
where:
- \(a_1\) is the amplitude of the first wave,
- \(a_2\) is the amplitude of the second wave,
- \(\phi\) is the phase difference between the two waves.

### Step 2: Substitute the Phase Difference
In this case, the phase difference \(\phi\) is given as \(2\pi\) radians. We can substitute this value into the formula:
\[ R = \sqrt{a_1^2 + a_2^2 + 2a_1a_2 \cos(2\pi)} \]

### Step 3: Calculate \(\cos(2\pi)\)
We know that:
\[ \cos(2\pi) = 1 \]
So, substituting this value into the equation gives:
\[ R = \sqrt{a_1^2 + a_2^2 + 2a_1a_2 \cdot 1} \]

### Step 4: Simplify the Expression
Now, we can simplify the expression:
\[ R = \sqrt{a_1^2 + a_2^2 + 2a_1a_2} \]

### Step 5: Recognize the Perfect Square
The expression inside the square root can be recognized as a perfect square:
\[ R = \sqrt{(a_1 + a_2)^2} \]

### Step 6: Final Result
Taking the square root gives us:
\[ R = a_1 + a_2 \]
Thus, the resultant amplitude when the phase difference is \(2\pi\) radians is simply the sum of the amplitudes of the two waves.

### Conclusion
The resultant amplitude \(R\) when the phase difference between the two waves is \(2\pi\) radians is:
\[ R = a_1 + a_2 \]

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