Question

To propagate both longitudinal and transverse waves, a material must have

• A. Bulk and shear moduli
• B. Only bulk modulus
• C. Only shear modulus
• D. Youngs and Bulk modulus

Answer 1

The Correct Option is A

To answer this question, we need to understand the mechanical properties required for the propagation of different types of waves in a material. Waves are disturbances that transfer energy from one point to another. In solid materials, two primary types of mechanical waves can propagate: longitudinal waves and transverse waves.

• Longitudinal Waves: These waves involve particle displacement parallel to the direction of wave propagation. They require a medium to resist compression, which is represented by the bulk \, modulus \, \left( K \right). The bulk modulus quantifies a material's response to uniform pressure, indicating its ability to resist volume changes.
• Transverse Waves: These waves involve particle displacement perpendicular to the direction of wave propagation. These require the medium to have shear resistance, measured by the shear \, modulus \, \left( G \right). The shear modulus measures how a material can resist shear stress, indicating its ability to maintain shape under deformation.

For a material to support both longitudinal and transverse waves, it must possess properties that enable both types of deformations. This means that the material must have both significant bulk modulus and shear modulus.

Now, let's assess the given options:

• Bulk and shear moduli: Correct, because both moduli are needed for the material to support both wave types.
• Only bulk modulus: Incorrect, as this would only support longitudinal waves.
• Only shear modulus: Incorrect, as this would only support transverse waves.
• Young's and Bulk modulus: Incorrect, as the Young's modulus is not directly responsible for transverse wave propagation; shear modulus is needed.

Therefore, the correct answer is: Bulk and shear moduli.