Question

For which of the following seismic waves the velocity is directly proportional to the shear strength of the material through which they pass?

• A. R-waves
• B. L-waves
• C. P-wave
• D. S-waves

Hint:

S-wave velocity depends on shear strength; they cannot travel through fluids due to zero shear modulus.

Answer 1

The Correct Option is D

In the study of seismic waves, it is crucial to understand the relationship between wave velocities and the properties of the materials they travel through. Among the different types of seismic waves, we focus on:

• R-waves (Rayleigh waves)
• L-waves (Love waves)
• P-waves (Primary waves)
• S-waves (Secondary waves)

The question asks which seismic wave has a velocity directly proportional to the shear strength of the material it traverses. Let's analyze each option:

1. R-waves: These are surface waves that cause the ground to ripple, much like water waves. They are influenced by the shear strength of near-surface materials but are more complex in their motion, being less directly proportional.
2. L-waves: Love waves result from shear horizontal motion and affect the surface. Their velocity is complex and influenced by surface conditions and material properties, not purely by shear strength.
3. P-waves: Also known as compressional waves, P-waves are longitudinal and travel through solids, liquids, and gases. Their velocity is primarily dependent on the elastic properties and density of materials, not directly on shear strength.
4. S-waves: These are transverse waves that only travel through solids. The velocity of S-waves is directly proportional to the shear modulus (a measure of shear strength) of the material, given by the formula:
   \( v_s = \sqrt{\frac{G}{\rho}} \)where \( v_s \) is the S-wave velocity, \( G \) is the shear modulus, and \( \rho \) is the density.

Based on the analysis above, the S-wave is directly proportional to the shear strength of the material it passes through. Thus, the correct answer is S-waves.