Which of the following statements is correct for stationary waves

Options

A. Nodes and antinodes are formed in case of stationary transverse wave only
B. In case of longitudinal stationary wave , compressions and rarefactions are obtained in place of nodes and antinodes respectively
C. Suppose two plane wave , one longitudinal and the other transverse having same frequency and amplitude are travelling in a medium in opposite directions with the same period , by superposition of these waves , stationary waves cannot be obtained
D. None of the above

Explanation

To determine which statement is correct regarding stationary waves, we can analyze each option step by step.

### Step 1: Understand the Definitions
- **Stationary Waves**: These are waves that do not propagate through the medium but instead oscillate in place, creating points of no displacement called nodes and points of maximum displacement called antinodes.

### Step 2: Analyze Each Option

**Option 1**: "Nodes and antinodes are found in case of stationary transverse wave only."
- **Analysis**: This statement is incorrect because nodes and antinodes can be found in both transverse and longitudinal stationary waves. Thus, this option is wrong.

**Option 2**: "In case of longitudinal stationary wave, compression and refraction are obtained in place of nodes and antinodes respectively."
- **Analysis**: This statement is also incorrect. In longitudinal waves, we have compressions (analogous to antinodes) and rarefactions (analogous to nodes), not "refraction." Thus, this option is wrong.

**Option 3**: "To obtain a stationary wave, two waves traveling in opposite directions having the same amplitude, same frequency are required."
- **Analysis**: This statement is correct. For stationary waves to form, two waves of the same amplitude and frequency must travel in opposite directions. They can be either both longitudinal or both transverse. Thus, this option is correct.

**Option 4**: (Not provided in the transcript, but we can assume it is incorrect based on the context).
- **Analysis**: Without the specific content of option 4, we cannot analyze it, but based on the previous analysis, we can conclude that option 3 is the only correct statement.

### Conclusion
The correct statement regarding stationary waves is **Option 3**.

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