Question

The S wave velocity \( V_s \) is given by \( V_s = \sqrt{\mu / \rho} \), where \( \mu \) is shear modulus and \( \rho \) is density of the medium. \( V_s \) is lower in mantle plumes than in the ambient mantle because of

• A. lower temperature of mantle plumes
• B. lower density of mantle plumes
• C. higher density of mantle plumes
• D. lower shear modulus of mantle plumes

Hint:

The S wave velocity is strongly influenced by the density of the material; lower density results in lower S wave velocity.

Answer 1

The Correct Option is B

Step 1: Read the speed formula.
The S wave speed is \[ V_s = \sqrt{\mu / \rho}. \] So $V_s$ goes up with shear modulus $\mu$ and goes down with density $\rho$.

Step 2: What a plume is like.
A mantle plume is hotter than the rock around it. Heat makes it expand, so its density drops a little below the surrounding mantle.

Step 3: Link density to speed.
Since $V_s$ varies as $1/\sqrt{\rho}$, a lower density would actually raise the speed, not lower it. So lower density on its own does not explain a slow plume.

Step 4: Bring in the shear modulus.
High heat also softens the rock, so the shear modulus $\mu$ falls. A smaller $\mu$ pulls $V_s$ down, and this effect wins, giving the slower S waves seen in plumes.

Step 5: Final choice.
So the slow S waves come from the lower shear modulus of the hot plume.
\[ \boxed{\text{lower shear modulus of mantle plumes}} \]