Match the following:Column-IColumn-II(a) Tran | vedclass

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(A) The speed of waves in different media is determined by the elastic properties and density of the medium.$(a)$ For a transverse wave in a solid (li

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$(a) - (ii), (b) - (i), (c) - (iv), (d) - (iii)$

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(A) The speed of waves in different media is determined by the elastic properties and density of the medium.$(a)$ For a transverse wave in a solid (like a steel rod), the speed is given by $v = \sqrt{\frac{\eta}{\rho}}$, where $\eta$ is the shear modulus and $\rho$ is the density. Thus, $(a) - (ii)$.$(b)$ For longitudinal waves in a bulk solid (like the earth's crust), the speed depends on both bulk modulus $B$ and shear modulus $\eta$: $v = \sqrt{\frac{B + \frac{4}{3}\eta}{\rho}}$. Thus, $(b) - (i)$.$(c)$ For longitudinal waves in a thin rod, the speed is given by $v = \sqrt{\frac{Y}{\rho}}$, where $Y$ is Young's modulus. Thus, $(c) - (iv)$.$(d)$ Ripples are surface waves on liquids where surface tension $T$ is the restoring force. The speed is given by $v = \sqrt{\frac{2 \pi T}{g \lambda}}$. Thus, $(d) - (iii)$.Therefore, the correct matching is $(a) - (ii), (b) - (i), (c) - (iv), (d) - (iii)$.

Column-$I$	Column-$II$
$(a)$ Transverse wave through a steel rod	$(i)$ $\sqrt{B + \frac{4}{3} \frac{\eta}{\rho}}$
$(b)$ Longitudinal waves in earth's crust	$(ii)$ $\sqrt{\frac{\eta}{\rho}}$
$(c)$ Longitudinal waves through a steel rod	$(iii)$ $\sqrt{\frac{2 \pi T}{g \lambda}}$
$(d)$ Ripples	$(iv)$ $\sqrt{\frac{Y}{\rho}}$

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