Question

If the velocity of the shear wave through a soil deposit is determined as $V_s$, the shear modulus 'G' is given as: (where, $\rho =$ mass density of soil)

• A. $\rho V$
• B. $\dfrac{\rho}{V_s}$
• C. $\rho V_s^2$
• D. $(\rho V_s)^{1/2}$

Hint:

Remember: $V_s = \sqrt{\dfrac{G}{\rho}}$. Always square $V_s$ when solving for $G$.

Answer 1

The Correct Option is C

Step 1: Recall the formula for shear modulus.
Shear modulus ($G$) is related to shear wave velocity ($V_s$) and density ($\rho$) by the equation: \[G = \rho V_s^2\]

Step 2: Derivation.
Starting with the formula for wave velocity, $V_s = \sqrt{\dfrac{G}{\rho}}$.
Squaring both sides and rearranging yields $G = \rho V_s^2$.

Step 3: Result.
The correct formula is $\rho V_s^2$.