Linear density of a string of is 1.3 x 10^-4 kg/m and wave equation is y = 0.021 sin (x + 30t ), Find, the tension in the string where, x in metre and t in second

0.12 N

0.21 N

1.2 N

0.012 N

Solution

0.12 N

Mass per unit length m = 1.3 × 10^-4 kg/m

y = 0.021 sin (x + 30t)

Comparing with y = a sin $(ωt + \frac{2 π x}{λ})$

a = 0.021, ω = 30

$2 πn = 30$

⇒ n = $\frac{30}{2 π}$

We know that

$\frac{2 π}{λ} = 1$

∴ $λ = 2 π$

Frequency,

n = $\frac{1}{λ} \sqrt{\frac{T}{m}}$

$\frac{30}{2 π} = \frac{1}{2 π} \sqrt{\frac{T}{1.3 \times 10^{- 4}}}$

T = 1.3 × 10^-4 × 900

T = 0.117

T = 0.12 N

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