Assertion: Two equations of wave are `y_(1)=A sin(omegat - kx) and y_(2) A sin(kx - omegat)`. These two waves have a phase difference of `pi`.
Reason: They are travelling in opposite directions.

Options

A. If both Assertion and Reason are true and the Reason is correct expanation of the Assertion.
B. If both Assertion and Reason are true but the Reason is not correct expanation of the Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the problem, we need to analyze the given wave equations and determine the validity of the assertion and the reason provided.

### Step-by-Step Solution:

1. **Identify the Wave Equations**:
The two wave equations given are:
- \( y_1 = A \sin(\omega t - kx) \)
- \( y_2 = A \sin(kx - \omega t) \)

2. **Rewrite the Second Equation**:
We can rewrite the second equation to match the form of the first:
- \( y_2 = A \sin(-(\omega t - kx)) \)
Using the property of sine, \( \sin(-x) = -\sin(x) \):
- \( y_2 = -A \sin(\omega t - kx) \)

3. **Determine the Phase Difference**:
The phase of \( y_1 \) is \( \omega t - kx \) and the phase of \( y_2 \) is \( -(\omega t - kx) \). The phase difference \( \Delta \phi \) can be calculated as:
- \( \Delta \phi = \phi_2 - \phi_1 = -(\omega t - kx) - (\omega t - kx) = -2(\omega t - kx) \)
At \( t = 0 \) and \( x = 0 \), the phase difference becomes:
- \( \Delta \phi = -2(0) = 0 \)
However, since \( y_2 = -A \sin(\omega t - kx) \), we can say that the two waves are indeed out of phase by \( \pi \) (since one is the negative of the other).

4. **Direction of Propagation**:
- The wave \( y_1 = A \sin(\omega t - kx) \) travels in the positive x-direction.
- The wave \( y_2 = A \sin(kx - \omega t) \) can be rewritten as \( y_2 = A \sin(-(\omega t - kx)) \), which indicates it travels in the negative x-direction.

5. **Conclusion**:
- The assertion is **true**: The two waves have a phase difference of \( \pi \).
- The reason is **true**: They are indeed traveling in opposite directions.

### Final Answer:
- Assertion: True
- Reason: True