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Q.

The linear density of a vibrating string is 1.3x10 ^-4 kg/m A transverse wave is propagating on the string and is described by the equation $y = 0 \cdot 021 \sin (x + 30 t)$ where x and y are measured in metre and t in second. The tension in the wire is

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a

0.48 N

b

1.20 N

c

4.80 N

d

0.12 N

answer is A.

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Detailed Solution

Given $y = 0 \cdot 021 \sin (x + 30 t)$
we know that $y = asin (ωt + kx)$
Comparing the two equations, we have
$ω = 30 and k = \frac{2 π}{λ} = 1 ∴ v = \frac{ω}{k} = 30 m / s Now v = \sqrt{(\frac{T}{m})} o r 30 = \sqrt{(\frac{T}{1 \cdot 3 \times 10^{- 4}})} or T = 0 \cdot 12 N$

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