Small amplitude progressive wave in a stretched string has a speed of `100 cm//s`.and frequency 100 Hz. The phase difference between two points 2.75 cm apart on the string in radians, is

Options

A. 0
B. `11pi//2`
C. `pi//4`
D. `3pi//8`

Explanation

To solve the problem of finding the phase difference between two points 2.75 cm apart on a stretched string with a wave speed of 100 cm/s and a frequency of 100 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Speed of the wave, \( v = 100 \, \text{cm/s} \)
- Frequency of the wave, \( f = 100 \, \text{Hz} \)
- Distance between two points, \( \Delta x = 2.75 \, \text{cm} \)

2. **Calculate the Wavelength (\( \lambda \)):**
- Use the formula for wave speed:
\[ v = f \cdot \lambda \]
- Rearranging gives:
\[ \lambda = \frac{v}{f} \]
- Substituting the values:
\[ \lambda = \frac{100 \, \text{cm/s}}{100 \, \text{Hz}} = 1 \, \text{cm} \]

3. **Calculate the Phase Difference (\( \Delta \phi \)):**
- The formula for phase difference is:
\[ \Delta \phi = \frac{2\pi}{\lambda} \cdot \Delta x \]
- Substituting the values we have:
\[ \Delta \phi = \frac{2\pi}{1 \, \text{cm}} \cdot 2.75 \, \text{cm} \]
- Simplifying this gives:
\[ \Delta \phi = 2\pi \cdot 2.75 = 5.5\pi \]

4. **Convert to Fractional Form:**
- We can express \( 5.5\pi \) as:
\[ 5.5\pi = \frac{11}{2}\pi \]

5. **Final Answer:**
- The phase difference between the two points is:
\[ \Delta \phi = \frac{11\pi}{2} \, \text{radians} \]

### Summary:
The phase difference between the two points 2.75 cm apart on the string is \( \frac{11\pi}{2} \) radians.