Geomechanics and Ground Control · Geomechanics · 2 marks · Numerical answer
Waves travel through the 100 mm long elastic isotropic cylindrical rock specimen from transmitter A to receiver B. Longitudinal and shear travel times are 0.025 ms and 0.04 ms. Find Poisson’s ratio to two decimals.
Speeds are vL=0.100/(0.025×10⁻³)=4000 m/s and vS=2500 m/s. The keyed solution uses the slender-bar longitudinal relation vL²=E/ρ and shear relation vS²=G/ρ. Since E=2G(1+ν), ν=vL²/(2vS²)−1=0.28. If “longitudinal” were interpreted as a bulk compressional wave, a different elastic-wave relation would give about 0.18; the bar-wave interpretation is stated explicitly here.
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