A cube (edge length L) of specific gravity' n' is suspended from a thin metal wire. The fundamental frequency for transverse standing waves in the wire is f₀. When the same cube is partially immersed in a liquid of specific gravity 2 upto a depth of 'h', the new fundamental frequency will be

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${(\frac{nL - 2 h}{L})}^{1 / 2} f_{0}$

${(\frac{L}{{nL}_{i} - 2 h})}^{1 / 2} f_{0}$

${(\frac{nL}{nL - 2 h})}^{1 / 2} f_{0}$

${(\frac{nL - 2 h}{nL})}^{1 / 2} f_{0}$

answer is B.

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Detailed Solution

$f \propto \sqrt{T}$

$T_{0} = {nρ}_{w} L^{3} g$

$T_{new} = {nρ}_{w} L^{3} g - 2 ρ_{w} L^{2} hg$

$= ρ_{w} L^{2} g (nL - 2 h)$

$∴ \frac{f_{n ew}}{f_{0}} = \sqrt{\frac{ρ_{w} L^{2} g (nL - 2 h)}{{nρ}_{ω} L^{3} g}}$

$f_{new} = {(\frac{nL - 2 h}{nL})}^{1 / 2} f_{0}$

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