(A): For the formation of stationary waves the medium must be bounded (having definite boundaries).
(R): In the stationary wave, some particles of the medium remain permanently at rest.

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To analyze the given statements regarding stationary waves, we can break down the solution into the following steps:

### Step 1: Understand the Assertion
The assertion states that "for the formation of stationary waves, the medium must be bounded (having definite boundaries)."
- **Explanation**: Stationary waves, also known as standing waves, require boundaries to reflect the waves back and forth. Without boundaries, the waves would continue to propagate indefinitely, preventing the formation of nodes and antinodes.

### Step 2: Understand the Reason
The reason provided is that "in the stationary wave, some particles of the medium remain permanently at rest."
- **Explanation**: In a stationary wave, certain points (nodes) do not oscillate, meaning the particles at these points remain at rest. This is a characteristic feature of stationary waves, where the interference of two waves traveling in opposite directions creates regions of no displacement (nodes).

### Step 3: Analyze the Relationship Between Assertion and Reason
Now we need to determine if the reason correctly explains the assertion.
- **Explanation**: While both the assertion and the reason are true, the reason does not provide a direct explanation for why the medium must be bounded. The assertion focuses on the necessity of boundaries for wave reflection, while the reason describes a characteristic of stationary waves.

### Step 4: Conclusion
Based on the analysis:
- The assertion is true: The medium must be bounded for stationary waves to form.
- The reason is also true: Some particles remain at rest in stationary waves.
- However, the reason does not explain the assertion. Therefore, we conclude that both statements are true, but the reason is not the correct explanation for the assertion.

### Final Answer
Both the assertion (A) and the reason (R) are true, but R is not the correct explanation for A.

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