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A transverse wave described by the equation $y = 0.02 Sin (x + 40 t)$ ( where x and t are in metres and seconds respectively) is travelling along a wire of area of cross section 1 $m m^{2}$ and density 8000 $k g / m^{3}$ . What is the tension in the string?

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20 N

12.8 N

30 N

14.4 N

answer is B.

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Detailed Solution

$\begin{array}{l} v = \frac{ω}{k} = 40 \\ \Rightarrow v = \sqrt{\frac{T}{μ}} \Rightarrow T = μ v^{2} = A ρ v^{2} \\ \Rightarrow T = 12.8 N \end{array}$

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