To analyze the two statements provided in the question, let's break down the concepts involved step by step.
### Step 1: Understanding Statement I
Statement I claims that the principle of superposition states that the amplitudes, velocities, and accelerations of particles in a medium due to the simultaneous operation of two or more progressive simple harmonic waves are the vector sum of the separate amplitudes, velocities, and accelerations from each wave acting alone.
**Explanation:**
- The principle of superposition is a fundamental concept in wave mechanics. It states that when two or more waves overlap in space, the resultant displacement at any point is equal to the sum of the displacements due to each individual wave.
- This principle applies not only to displacement but also to velocity and acceleration, which are derived from displacement. Thus, the statement correctly describes the principle of superposition.
### Step 2: Understanding Statement II
Statement II states that amplitudes, velocities, and accelerations are linear functions of the displacement of the particle and its time derivatives.
**Explanation:**
- In wave mechanics, the displacement of a particle can be expressed as a function of time. The first derivative of displacement with respect to time gives velocity, and the second derivative gives acceleration.
- Since these relationships are linear (i.e., the velocity is directly proportional to displacement, and acceleration is directly proportional to velocity), this statement is also true.
### Step 3: Analyzing the Relationship Between the Two Statements
Now, we need to determine if Statement II explains Statement I.
**Explanation:**
- If we take the displacement due to multiple waves (as described in Statement I) and differentiate it with respect to time, we can derive the velocities due to each wave and then sum them up to find the net velocity.
- Similarly, differentiating the velocity expressions will yield the net acceleration.
- Therefore, Statement II provides a mathematical foundation that supports the claims made in Statement I, showing how the linear relationships allow for the application of the principle of superposition.
### Conclusion
Both statements are true, and Statement II does explain Statement I. Thus, the correct conclusion is that both statements are true, and Statement II correctly explains Statement I.
### Final Answer
- Statement I: True
- Statement II: True
- Statement II explains Statement I: True
---
