Which of the following statements are true wave motion? a) Mechanical transverse waves can propagate through all mediums. b) Longitudinal waves can propagate through solids only c) Mechanical transverse waves can propagate through only d) Longitudinal waves can propagate through vacuum.

Options

A. Mechanical transverse waves can propagate through all mediums.
B. Longitudinal waves can propagate through solids only
C. Mechanical transverse waves can propagate through only
D. Longitudinal waves can propagate through vacuum.

Explanation

To determine which statements about wave motion are true, let's analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement A: Mechanical transverse waves can propagate through all mediums.**
- **Analysis:** This statement is false. Mechanical transverse waves, such as waves on a string, can only propagate through solids. They cannot propagate through fluids (liquids and gases) because there is no mechanism to support the perpendicular motion required for transverse waves.
- **Conclusion:** **False**

2. **Statement B: Longitudinal waves can propagate through solids only.**
- **Analysis:** This statement is also false. Longitudinal waves can propagate through all states of matter: solids, liquids, and gases. They involve particle motion parallel to the direction of wave propagation, which can occur in all mediums.
- **Conclusion:** **False**

3. **Statement C: Mechanical transverse waves can propagate through only solids.**
- **Analysis:** This statement is true. As previously mentioned, mechanical transverse waves require a medium that can support shear stress, which is only available in solids. They cannot propagate through liquids or gases.
- **Conclusion:** **True**

4. **Statement D: Longitudinal waves can propagate through vacuum.**
- **Analysis:** This statement is false. Longitudinal waves require a medium to propagate, as they involve the compression and rarefaction of particles. In a vacuum, there are no particles to transmit the wave.
- **Conclusion:** **False**

### Final Summary:
- **Statement A:** False
- **Statement B:** False
- **Statement C:** True
- **Statement D:** False

The only true statement is **C: Mechanical transverse waves can propagate through only solids.**

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