118. An isotropic, homogeneous sample is subjected
to uniaxial stress along the x-axis. The absolute
value of the axial strain is found to be thrice the
normal strain. The ratio (Vp/Vs) of the P wave
and S wave velocity is
1. 1.5
2. 1.75
3. 2.0
4. 2.25
Solution:
Poisson's ratio is defined as the negative of the ratio of the lateral strain to the axial strain for a uniaxial stress state.
Poisson's ratio (ν ) = \frac{normal strain}{axial strain}
From the above problem, axial strain = 3 normal strain
ν =\frac{1}{3}
ν =\frac{1}{3}
\frac{1}{3} = \frac{normal strain}{axial strain}
The relation between velocities of P and S-waves and Poisson's ratio is given below
\frac{V_{p}}{V_{s}} =\sqrt\frac{2(1-ν)}{(1-2ν)}
The relation between velocities of P and S-waves and Poisson's ratio is given below
\frac{V_{p}}{V_{s}} =\sqrt\frac{2(1-ν)}{(1-2ν)}
\frac{V_{p}}{V_{s}}=\sqrt\frac{2(1-\frac{1}{3})}{(1-2*\frac{1}{3})}
\frac{V_{p}}{V_{s}} =\sqrt4
\frac{V_{p}}{V_{s}} =2
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