A sonometer wire is in unison with a tuning f | vedclass

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(B) For a sonometer,the frequency of vibration $n$ is proportional to the square root of the tension $T$,i.e.,$n \propto \sqrt{T}$.When the weight is

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$\frac{n}{n-x}=\sqrt{\frac{d}{d-1}}$

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(B) For a sonometer,the frequency of vibration $n$ is proportional to the square root of the tension $T$,i.e.,$n \propto \sqrt{T}$.When the weight is in air,the tension $T_1 = V \cdot d \cdot \rho_w \cdot g$,where $V$ is the volume of the weight,$d$ is its specific gravity,and $\rho_w$ is the density of water.Thus,$n \propto \sqrt{V \cdot d \cdot \rho_w \cdot g}$.When the weight is immersed in water,the effective weight (tension) becomes $T_2 = V \cdot (d - 1) \cdot \rho_w \cdot g$ due to the buoyant force.The new frequency $n'$ is given by $n' = n - x$ (since beats are produced).Thus,$n' \propto \sqrt{V \cdot (d - 1) \cdot \rho_w \cdot g}$.Taking the ratio of the two frequencies:$\frac{n}{n-x} = \sqrt{\frac{V \cdot d \cdot \rho_w \cdot g}{V \cdot (d - 1) \cdot \rho_w \cdot g}}$$\frac{n}{n-x} = \sqrt{\frac{d}{d-1}}$.

$A$ sonometer wire is in unison with a tuning fork of frequency '$n$' when it is stretched by a weight of specific gravity '$d$'. When the weight is completely immersed in water,'$x$' beats are produced per second,then

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