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A transverse wave is passing through a light string shown in the figure. The equation of wave is $y = Asin (ωt - kx)$ . The area of cross-section of string is A and density is $ρ .$ The hanging mass is

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$\frac{{ρAω}^{2}}{k^{2} g}$

$\frac{ω}{kg}$

$Aω$

$\frac{k^{2} g}{ω}$

answer is C.

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Detailed Solution

$V_{ω} = \frac{ω}{k} = \sqrt{\frac{T}{Aρ}}$

$\Rightarrow \frac{ω^{2}}{k^{2}} = \frac{mg}{Aρ}$

$\Rightarrow \frac{ω^{2} Aρ}{k^{2} g} = m$

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