The bulk modulus and modulus of rigidity for aluminium are $7.5 imes 10^{10}$ Nm$^{-2}$ and $2.1 imes 10^{10}$ Nm$^{-2}$, respectively. Determine the velocity of the waves in the medium. Density of aluminium is $2.7 imes 10^3$ kg m$^{-3}$.

Question

The bulk modulus and modulus of rigidity for aluminium are $7.5 	imes 10^{10}$ Nm$^{-2}$ and $2.1 	imes 10^{10}$ Nm$^{-2}$, respectively. Determine the velocity of the waves in the medium. Density of aluminium is $2.7 	imes 10^3$ kg m$^{-3}$.

Aicharya · Accepted Answer

Sol. Given, bulk modulus, $B = 7.5 	imes 10^{10}$ Nm$^{-2}$ Modulus of rigidity, $\eta = 2.1 	imes 10^{10}$ Nm$^{-2}$ Density, $ho = 2.7 	imes 10^3$ kg m$^{-3}$ Velocity of longitudinal waves in aluminium, $v = \sqrt{\dfrac{B + 	frac{4}{3}\eta}{ho}} = \sqrt{\dfrac{7.5 	imes 10^{10} + 	frac{4}{3} 	imes 2.1 	imes 10^{10}}{2.7 	imes 10^3}}$ $v = 6.18 	imes 10^3$ ms$^{-1}$ Answer: $6.18 	imes 10^3$ ms$^{-1}$

The bulk modulus and modulus of rigidity for aluminium are $7.5 \times 10^{10}$ Nm$^{-2}$ and $2.1 \times…

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