Step 1: Recall the properties of waves in materials
To propagate both longitudinal and transverse waves, the material must possess certain mechanical properties. The longitudinal waves (or compression waves) require the material to resist compression, and transverse waves (or shear waves) require the material to resist shearing.
Step 2: Understand the requirements for wave propagation
- Longitudinal waves: These waves propagate through the material by compressing and expanding the material in the direction of the wave. The ability to propagate longitudinal waves depends on the bulk modulus, which measures the material's resistance to uniform compression.
- Transverse waves: These waves move perpendicular to the direction of the wave. The ability to propagate transverse waves depends on the shear modulus (also known as the modulus of rigidity), which measures the material's resistance to shearing or deformation.
Step 3: Combine the necessary moduli
- Bulk modulus is needed for longitudinal wave propagation, as it resists compression.
- Shear modulus is required for transverse wave propagation, as it resists shearing.
Thus, for a material to support both types of waves, it must have both bulk modulus and shear modulus.
Final Answer:
The material must have both bulk and shear moduli to propagate both longitudinal and transverse waves. This matches option (D).
Longitudinal waves are waves where the displacement of the medium is in the same direction as, or the opposite direction to, the direction of propagation of the wave. These waves require a medium with non-zero bulk modulus, which represents the resistance to compression.
Transverse waves are waves where the displacement of the medium is at right angles to the direction of propagation of the wave.
These waves require a medium with a non-zero shear modulus, which represents resistance to deformation by shearing.
To propagate both longitudinal and transverse waves, a material must have both bulk and shear moduli.
Solids typically possess both, while fluids (liquids and gases) only have a bulk modulus.
The correct answer is (D) Bulk and shear moduli.