Which of the following waves does not require any material medium for their propagation?

Options

A. Sound waves
B. Radio waves
C. X-rays
D. Both (b) and (c )

Explanation

**Step-by-Step Solution:**

1. **Understanding Wave Propagation**:
- Waves can be classified based on whether they require a material medium for their propagation or not.
- Waves that require a medium (like air, water, or solids) are called mechanical waves, while those that do not require a medium are called electromagnetic waves.

2. **Identifying the Types of Waves**:
- The question provides us with three types of waves: sound waves, radio waves, and X-rays.
- We need to analyze each of these waves to determine whether they require a medium for propagation.

3. **Analyzing Sound Waves**:
- Sound waves are mechanical waves that require a medium (like air, water, or solids) to travel.
- They are longitudinal waves, meaning the oscillation of particles occurs in the same direction as the wave travels.

4. **Analyzing Radio Waves**:
- Radio waves are a type of electromagnetic wave.
- They do not require a material medium for propagation; they can travel through a vacuum (space).

5. **Analyzing X-Rays**:
- X-rays are also electromagnetic waves.
- Similar to radio waves, they do not require a medium for propagation and can also travel through a vacuum.

6. **Conclusion**:
- Based on the analysis, both radio waves and X-rays do not require a material medium for their propagation.
- Therefore, the correct answer is option 4, which states that both radio waves and X-rays do not require a medium.

**Final Answer**: Option 4 (Radio Waves and X-Rays) does not require any material medium for their propagation.

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