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: Understanding S wave velocity.
The velocity of S-waves in a medium is determined by both the shear modulus \( \mu \) (a measure of the medium’s resistance to shear deformation) and the density \( \rho \). The equation \( V_s = \sqrt{\mu / \rho} \) shows that higher shear modulus or lower density results in higher S wave velocity. Conversely, lower shear modulus or higher density leads to lower S wave velocity.

Step 2: Analyzing the effect of density on \( V_s \).
Since \( V_s \) is inversely proportional to the square root of the density \( \rho \), a lower density results in a lower S wave velocity. Mantle plumes are generally characterized by lower density compared to the ambient mantle due to their higher temperature, which causes thermal expansion. This lower density reduces the S wave velocity.

Step 3: Analyzing temperature and shear modulus.
- (A) Lower temperature of mantle plumes: While the temperature in mantle plumes is higher, this would decrease the shear modulus rather than directly affecting the density. However, the primary effect on \( V_s \) comes from the density difference.
- (B) Lower density of mantle plumes: As explained, lower density in mantle plumes leads to a reduction in S wave velocity because of the inverse relationship between velocity and density.
- (C) Higher density of mantle plumes: This is incorrect since mantle plumes have lower density compared to the surrounding mantle.
- (D) Lower shear modulus of mantle plumes: While a lower shear modulus could also decrease \( V_s \), the dominant factor is the lower density of the mantle plumes.

Step 4: Conclusion.
The primary reason for the lower S wave velocity in mantle plumes is their lower density compared to the ambient mantle. Hence, the correct answer is (B).
\[ \boxed{\text{lower density of mantle plumes}} \]