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(A) In a solid medium,both longitudinal and transverse waves can propagate.$1$. Longitudinal waves involve compression and rarefaction,which depend on

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Due to different elastic moduli involved.

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(A) In a solid medium,both longitudinal and transverse waves can propagate.$1$. Longitudinal waves involve compression and rarefaction,which depend on the bulk modulus $(B)$ and the shear modulus $(G)$ of the material. The speed is given by $v_L = \sqrt{\frac{B + \frac{4}{3}G}{\rho}}$,where $\rho$ is the density.$2$. Transverse waves involve shearing of the material,which depends only on the shear modulus $(G)$. The speed is given by $v_T = \sqrt{\frac{G}{\rho}}$.$3$. Since the elastic properties (bulk modulus and shear modulus) of a solid are different,the speeds of these two types of waves are inherently different.

Why are the speeds of longitudinal and transverse waves in a solid different? Explain.

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