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A string is producing transverse vibration whose equation is $y = 0.021 \sin (x + 30 t)$ , Where x and y are in meters and t is in seconds. If the linear density of the string is $1 .3 \times 10^{- 4}$ kg/m, then the tension in the string in N will be

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0.5

0.117

answer is D.

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Detailed Solution

$y = 0 .021 \sin (x + 30 t) \Rightarrow v = \frac{ω}{k} = \frac{30}{1} = 30 m / s$
Using, $v = \sqrt{\frac{T}{m}} \Rightarrow 30 = \sqrt{\frac{T}{1 .3 \times 10^{- 4}}} \Rightarrow T = 0 .117 N$

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