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Elasticity in Crystals
The Determination of Velocity of Propagation
Dynamic Resonance Method for Measuring the Elastic Moduli
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acoustic acoustic impedance adiabatic amplitude Anderson applied pulse axes axis Block diagram buffer rod bulk modulus calculated Ceram circuit classes coefficients components compressibility computed cēs cross section cubic crystal cubic system cylinder Debye temperature delay density determined differential displacement dynamic echo elastic compliances elastic constants elastic moduli elastic properties energy equation expressed flexural vibration frequency counter function given internal friction isothermal isotropic isotropic materials kbar length longitudinal wave matrix McSkimin measurements motion notation obtained oscillator oscilloscope oscillotor parameter percent phase Phys Poisson's ratio polycrystalline precision pressure derivatives propagation quartz reduced relation resonance method resonant frequency shear modulus shear velocity shown in Fig signal Single Crystal Soga solid solution sound velocity sphere Spinner strain symmetry operations Table technique Tefft tensor thermodynamic third-order torsional transducer triclinic Ultrasonic Wachtman Young's modulus zero