A transverse wave described by

$y = (0.02 m) s i n [(1.0 m^{- 1}) x + (30 s^{- 1}) t]$

propagates on a stretched string having a linear mass density of $1.2 \times 10^{- 4} k g m^{- 1}$ . Find the tension in the string.

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Solution

m = mass per unit length

$= 1.2 \times 10^{- 4} k g / m$

Y = (0.02 m) sin

$[1.0 m^{- 1} x + (30 s^{- 1}) t]$

Here, $k = 1 m^{- 1} = \frac{2 π}{λ}$

$w = 30 s^{- 1} = 2 π f$

$∴$ Velocity of the wave in the stretched string

$v = λ f = \frac{ω}{k} = \frac{30}{I}$

$= 30 m / s$

$\Rightarrow v = (\frac{T}{m})$

$\Rightarrow 30 = \sqrt{(\frac{T}{1.2} \times 10^{- 4} N)}$

$\Rightarrow t = 10.8 \times 10^{- 2} N$

$\Rightarrow T = 0.08$ Newton

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