Calculate the velocity of a compressional wave in a homogeneous rock layer with a density of 2.6 g/cm3 , a Young’s modulus of 0.39✕1011 N/m2 , and a Poisson’s ratio of 0.11

Respuesta :

Answer:

V = 2534.37 m/s

Explanation:

density [tex]= 2.6 g/cm^3 = 2600 kg/m^3[/tex]

young's modulus [tex]= 0.39\times 10^{11} N/m^2[/tex]

Poisson's ratio = 0.11

we know that bulk modulus is given as

[tex]\beta = \frac{E}{3(1-2\mu)}[/tex]

         [tex]= \frac{0.39\times 10^{11}}{3(1-2\times 0.11)}[/tex]

        [tex] = 1.67\times 10^{10}[/tex]

velocity of wave is given as

[tex]V =\sqrt{\frac{\beta}{\rho}}[/tex]

[tex]V = \sqrt{\frac{1.67\times 10^{10}}{2600}}[/tex]

V = 2534.37 m/s