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A transverse wave described by equation $y = 0.02 \sin (x + 30 t)$ (where x and t are in metres and seconds, respectively) is travelling along a wire of area of cross-section 1 ${mm}^{2}$ and density 8000 $kg / m^{3}$ . What is the tension in the string?

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20 N

7.2 N

30 N

14.4 N

answer is B.

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Detailed Solution

$y = 0.02 \sin (x + 30 t)$

For the given wave:

(x+30t = constant)

$v = \frac{dx}{dt} = - 30$

$We have v = \sqrt{\frac{T}{μ}} \Rightarrow T = {μv}^{2} = A . {ρV}^{2}$

= $(10^{- 6} m^{2}) (8 \times 10^{3} \frac{kg}{m^{3}}) {(30)}^{2}$

$\Rightarrow T = 7.2 N$

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