(A): In a mechanical progressive wave, energy is transferred from one point to the other.
(R): In a mechanical progressive wave energy transfer takes place because of the coupling through elastic forces between neighbouring oscillating particles of the medium.

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 solve the question, we need to analyze the statement (A) and the reason (R) provided.

### Step-by-Step Solution:

1. **Understanding Statement (A)**:
- The statement (A) claims that in a mechanical progressive wave, energy is transferred from one point to another.
- This is true because mechanical waves, such as sound waves or waves on a string, involve the transfer of energy through the medium as the wave propagates.

2. **Understanding Statement (R)**:
- The reason (R) states that in a mechanical progressive wave, energy transfer occurs due to coupling through elastic forces between neighboring oscillating particles of the medium.
- This is also true. When a wave travels through a medium, the particles of the medium oscillate around their equilibrium positions. The oscillation of one particle affects its neighboring particles due to elastic forces (like tension in a string or pressure in a fluid), causing them to oscillate as well.

3. **Establishing the Relationship Between (A) and (R)**:
- Since both statements (A) and (R) are true, we need to determine if (R) correctly explains (A).
- The coupling through elastic forces indeed explains how energy is transferred from one particle to another, which leads to the propagation of the wave. Thus, (R) provides a valid explanation for (A).

4. **Conclusion**:
- Both statement (A) and reason (R) are true, and (R) is the correct explanation of (A).

### Final Answer:
Both (A) and (R) are true, and (R) is the correct explanation of (A).

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