A hollow pipe of length $0.8 m$ is closed at one end. At its open end a $0.5 m$ 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 $50 N$ and the speed of sound is $320 m s^{- 1}$ , the mass of the string is

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$10 g$

$20 g$

$5 g$

$40 g$

answer is B.

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Detailed Solution

$\frac{v_{s}}{4 L_{P}} = \frac{2}{2 l_{S}} \sqrt{\frac{T}{μ}} \Rightarrow \frac{320}{4 \times 0.8} = \frac{1}{0.5} \sqrt{\frac{50}{μ}} \Rightarrow μ = \frac{1}{50}$
Mass of string, $m = μ l_{S} = \frac{1}{50} \times 0.5 = 0.01 k g = 10 g$

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