A wavefront is represented by the plane `y = 3 - x`. The propagation of wave takes place at

Options

A. `45^@` with x - direction
B. `135^@C` with x-direction
C. `60^@` with x-direction
D. No sufficient data

Answer

To solve the problem, we need to analyze the given wavefront represented by the equation \( y = 3 - x \). We will determine the direction of wave propagation based on this wavefront.

### Step-by-Step Solution:

1. **Identify the Wavefront Equation**:
The wavefront is given by the equation:
\[ y = 3 - x \]
This can be rewritten as:
\[ y = -x + 3 \]
This is a linear equation representing a straight line in the xy-plane.

2. **Determine the Slope of the Wavefront**:
From the equation \( y = -x + 3 \), we can see that the slope (m) of the line is:
\[ m = -1 \]

3. **Calculate the Angle of the Wavefront**:
The angle \( \theta \) that the wavefront makes with the positive x-axis can be found using the tangent of the slope:
\[ \tan(\theta) = \text{slope} = -1 \]
Therefore, the angle \( \theta \) can be calculated as:
\[ \theta = \tan^{-1}(-1) = 135^\circ \]
This angle is measured from the positive x-axis in the counter-clockwise direction.

4. **Determine the Direction of Wave Propagation**:
The wave propagates perpendicular to the wavefront. Since the wavefront has an angle of \( 135^\circ \), the direction of propagation will be at an angle of:
\[ \text{Direction of propagation} = 135^\circ - 90^\circ = 45^\circ \]
This means the wave propagates at \( 45^\circ \) to the positive x-axis.

5. **Conclusion**:
The direction of wave propagation is \( 45^\circ \) from the positive x-axis.

### Final Answer:
The propagation of the wave takes place at an angle of \( 45^\circ \) from the positive x-axis.