Staement I: pressure and density change do not occure in a transverse stationary wave.
Statement II: the average distance between any two particles of the wave remains the same.

Options

A. Statement I is true, statement II is true and statement II is the correct explaination for statement I.
B. Statement I is true, statement II is true and statement II is NOT the correct explaination for statement I.
C. Statement I is true, statement II is false.
D. Statement I is false, statement II is true.

Explanation

To analyze the given statements about transverse stationary waves, let's break down the problem step by step.

### Step 1: Understanding Transverse Stationary Waves
Transverse stationary waves are formed when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. In such waves, particles of the medium move perpendicular to the direction of wave propagation.

**Hint:** Recall the definition of transverse waves and how they are formed through interference.

### Step 2: Evaluating Statement I
**Statement I:** "Pressure and density change do not occur in a transverse stationary wave."

In a transverse stationary wave, the energy remains confined within certain regions (nodes and antinodes). Since there is no net movement of energy in one direction, there are no compressions or rarefactions, which means that pressure and density do not change.

**Conclusion for Statement I:** This statement is **true**.

**Hint:** Think about how energy distribution in stationary waves differs from traveling waves.

### Step 3: Evaluating Statement II
**Statement II:** "The average distance between any two particles of the wave remains the same."

In a transverse stationary wave, particles oscillate about their equilibrium positions, but the overall average distance between any two particles does not change. The nodes (points of no displacement) and antinodes (points of maximum displacement) remain fixed, ensuring that the average distance between particles remains constant.

**Conclusion for Statement II:** This statement is also **true**.

**Hint:** Consider how the motion of particles in a wave affects their relative positions.

### Step 4: Analyzing the Relationship Between the Statements
While both statements are true, we need to determine if one statement explains the other.

- Statement I (no pressure and density change) does not directly explain why the average distance between particles remains the same (Statement II). They are related concepts but do not provide a cause-and-effect relationship.

**Conclusion:** Both statements are true, but Statement II is not the correct explanation of Statement I.

### Final Answer
Both statements are true, but Statement II is not the correct explanation of Statement I.

### Summary of the Solution:
1. **Statement I** is true because pressure and density do not change in a transverse stationary wave.
2. **Statement II** is true because the average distance between particles remains constant.
3. Both statements are true, but Statement II does not explain Statement I.

**Final Answer:** Both statements are true, but Statement II is not the correct explanation of Statement I.