The ratio of radii of two wires is 1: 2 and t | vedclass

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(D) The speed of a transverse wave in a stretched wire is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass de

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$4: 1$

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(D) The speed of a transverse wave in a stretched wire is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Linear mass density $\mu = \frac{	ext{mass}}{	ext{length}} = \frac{ho 	imes 	ext{Volume}}{	ext{length}} = ho 	imes A = ho 	imes \pi R^2$,where $ho$ is the material density and $R$ is the radius of the wire.Substituting $\mu$ in the velocity formula: $v = \sqrt{\frac{T}{ho \pi R^2}}$.Given the ratio of radii $\frac{R_1}{R_2} = \frac{1}{2}$ and the ratio of densities $\frac{ho_1}{ho_2} = \frac{1}{4}$.Since the tension $T$ is the same for both wires,the ratio of speeds is:$\frac{v_1}{v_2} = \sqrt{\frac{ho_2}{ho_1} 	imes \frac{R_2^2}{R_1^2}}$$\frac{v_1}{v_2} = \sqrt{\left(\frac{4}{1}ight) 	imes \left(\frac{2}{1}ight)^2} = \sqrt{4 	imes 4} = \sqrt{16} = 4$.Thus,the ratio is $4: 1$.

The ratio of radii of two wires is $1: 2$ and the ratio of the densities of their materials is $1: 4$. If the same tension is applied to both wires,then the ratio of the speed of transverse waves produced in them is

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