What is the relation between young's modulus of elasticity and density of the material used?

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W.r.t. civil engineering structure especially concrete

Check out the relation between speed of sound, isentropic bulk modulus and density of an (isotropic) material. The bulk modulus in turn is related to the elastic properties.Specifically the bulk modulus and the Poisson ratio determine Young's modulus. If you like you, can use this relation and replace the bulk modulus as a function of density and speed of sound. Then you have the dependence you are looking for I guess.

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