GATE-2018 (24) :Wyllie – Time average equation

GATE-2007

Q 46):The Poisson's ratio of a rock with P- and S- wave velocities in the ratio of √3:1 is..

solution

Formula: -

The relation between Poisson's ratio and velocities of P- and S- wave are 
  
$\frac{V_P}{V_S}=\sqrt{\frac{2(1-\nu)}{1-2\nu}}$ ---(1)

Vp – velocity of P- wave

Vs – velocity of S- wave

ν – poisson’s ratio

so, substitute the P and S wave velocity ratio’s in above equation

2(1-ν) / (1-2ν) =3/1

2-2ν = 3 – 6ν

4ν =1

ν = 1 / 4

Therefore ν = 0.25 (poisson’s ratio is a dimensionless quantity).