Volume Strain

Show that the volume that the volume strain in any longitudinal wave is given by (-dy/dx), where y is the displacement at the plane x. Hence show that for a harmonic wave of amplitude A and wavelength lambda in a medium of elasticity E, the excess pressure is given by p=EA(2pi)/(lambda)sin2pi((t)/(T) - (x)/(lambda)) Deduce the pressure amplitude, if E=1.6xx10^(3)Nm^(-2), A=4xx10^(-7)m and lambda=0.5m .

Elasticity: Longitudinal Stress & strain | Shear stress & shear strain | Volumetric stress and strain

Define Strain Energy. Derive expressions for (i) work done per unit volume (ii) Strain energy per unit volume. OR Derive an expression for strain energy per unit volume of the material of a wire.

Derive an expression for strain energy and show that the strain energy per unit volume of a stretched wire is proportional to the square of the strain.

The elastic energy per unit volume is terms of longitudinal strain sigma and Young's modulus Y is