Transverse waves propagate in a medium with

Options

A. shear modulus of elasticity
B. bulk modulus of elasticity
C. modulus of rigidity
D. compressibility of the medium

Answer

To solve the question regarding the propagation of transverse waves in a medium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Transverse Waves**:
- Transverse waves are waves where the particle displacement is perpendicular to the direction of wave propagation. Examples include waves on a string or seismic S-waves.

2. **Identifying the Medium**:
- Transverse waves can only propagate in solids. This is because solids can resist shear stress, which is necessary for the formation of transverse waves. In contrast, liquids and gases cannot support shear stress.

3. **Reviewing the Given Options**:
- The options provided are:
- A) Shear modulus of elasticity
- B) Bulk modulus of elasticity
- C) Modulus of rigidity
- D) Compressibility of the medium

4. **Analyzing Each Option**:
- **Shear Modulus of Elasticity**: This measures the material's ability to resist shear deformation. It is relevant for solids and is the correct choice for transverse wave propagation.
- **Bulk Modulus of Elasticity**: This measures a material's response to uniform pressure and is applicable to liquids and gases, not solids.
- **Modulus of Rigidity**: This is another term for shear modulus, which also applies to solids.
- **Compressibility**: This refers to how much a substance can be compressed and is relevant for fluids, not solids.

5. **Conclusion**:
- Since transverse waves propagate in solids and are associated with shear deformation, the correct answer is the **shear modulus of elasticity**.

### Final Answer:
Transverse waves propagate in a medium with **shear modulus of elasticity**.