A hollow pipe of length $0.8 \mathrm{~m}$ is closed at one end. At its open end a $0.5 \mathrm{~m}$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \mathrm{~N}$ and the speed of sound is $320 \mathrm{~ms}^{-1}$, the mass of the string is
IIT 2010, Advanced
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$ \frac{\mathrm{v}_{\mathrm{S}}}{4 \mathrm{~L}_{\mathrm{P}}}=\frac{2 \sqrt{\frac{\mathrm{T}}{\mu}}}{2 \ell_{\mathrm{S}}} $
$ \mu \ell_{\mathrm{S}}=10 \ \mathrm{gm}$
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