If path difference between is `(11 lambda)/(4)` then the phase difference between two waves will be

Options

A. `11 pi //2`
B. ` 5 pi//2`
C. `13pi//2`
D. `7pi//2`

Explanation

To find the phase difference between two waves given a path difference of \(\frac{11 \lambda}{4}\), we can use the formula that relates path difference to phase difference.

### Step-by-Step Solution:

1. **Identify the formula**: The phase difference \(\phi\) is related to the path difference \(\Delta x\) by the formula:
\[ \phi = \frac{2\pi}{\lambda} \Delta x \]
where \(\lambda\) is the wavelength of the waves.

2. **Substitute the given values**: We know the path difference \(\Delta x = \frac{11 \lambda}{4}\). Substitute this into the formula:
\[ \phi = \frac{2\pi}{\lambda} \left(\frac{11 \lambda}{4}\right) \]

3. **Simplify the expression**: The \(\lambda\) in the numerator and denominator cancels out:
\[ \phi = \frac{2\pi \cdot 11}{4} \]

4. **Calculate the phase difference**: Simplifying further gives:
\[ \phi = \frac{22\pi}{4} = \frac{11\pi}{2} \]

5. **Final result**: Therefore, the phase difference between the two waves is:
\[ \phi = \frac{11\pi}{2} \]