The phase difference between oscillatory motion of two points separated by a distance of `lamda/2` is ( where `lamda` is the wavelength)

Options

A. `pi/2`
B. `pi`
C. `(3pi)/2`
D. `2pi`

Explanation

To find the phase difference between the oscillatory motion of two points separated by a distance of \( \frac{\lambda}{2} \), we can use the relationship between phase difference and path difference. Here’s the step-by-step solution:

### Step 1: Understand the relationship
The phase difference \( \Delta \phi \) between two points in a wave is related to the path difference \( \Delta x \) by the formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \cdot \Delta x \]
where \( \lambda \) is the wavelength of the wave.

### Step 2: Identify the path difference
In this case, the path difference \( \Delta x \) is given as \( \frac{\lambda}{2} \).

### Step 3: Substitute the path difference into the formula
Now, we can substitute \( \Delta x = \frac{\lambda}{2} \) into the phase difference formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \cdot \left(\frac{\lambda}{2}\right) \]

### Step 4: Simplify the expression
Now simplify the expression:
\[ \Delta \phi = \frac{2\pi \cdot \lambda}{2 \cdot \lambda} = \frac{2\pi}{2} = \pi \]

### Conclusion
Thus, the phase difference between the oscillatory motion of the two points separated by a distance of \( \frac{\lambda}{2} \) is:
\[ \Delta \phi = \pi \]

### Final Answer
The phase difference is \( \pi \).