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The mass per unit length of a uniform wire is 0.135g/cm. A transverse wave of the form $y = - 0.21 \sin (x + 30 t)$ is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is $x \times 10^{- 2}$ N. Value of x is________(Round-off to the nearest integer)

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answer is 1215.

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Detailed Solution

$\begin{array}{l} Wave velocity, v = \frac{ω}{k} = \frac{30}{1} = 30 m / s \\ Also, wave velocity on string = v = \sqrt{\frac{T}{μ}} \\ \Rightarrow T = μ v^{2} = 0.135 \times 10^{- 1} \times 900 \\ \Rightarrow T = 12.15 = 1215 \times 10^{- 2} N \\ \Rightarrow x = 1215 \end{array}$

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The mass per unit length of a uniform wire is 0.135g/cm. A transverse wave of the form y=−0.21 sinx+30t is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x×10−2 N. Value of x is________(Round-off to the nearest integer)