Question
A transverse wave described by
$\text{y}=(0.02\text{m})\sin\Big[(1.0\text{m}^{-1})\text{x}+(30\text{s}^{-1})\text{t}\Big]$
propagates on a stretched string having a linear mass density of 1.2 x 10-4kg/m. Find the tension in the string.✓
Answer
m = mass per unit length $=1.2\times10^{-4}\text{kg/mt}$
$\text{y}=(0.02\text{m})\sin\Big[(1.0\text{m}^{-1})\text{x}+(30\text{s}^{-1})\text{t}\Big]$
Here, $\text{k}=1\text{m}^{-1}=\frac{2\pi}{\lambda}$$\omega=30\text{s}^{-1}=2\pi\text{f}$
$\therefore\ $velocity of the wave in the stretched string
$\text{v}=\lambda\text{f}=\frac{\omega}{\text{k}}=\frac{30}{\text{I}}=30\text{m/s}$
$\Rightarrow\text{v}=\sqrt{\frac{\text{T}}{\text{m}}}$
$\Rightarrow30\sqrt{\Big(\frac{\text{T}}{1.2}\Big)\times10^{-4}\text{N}}$
$\Rightarrow\text{T}=10.8\times10^{-2}\text{N}$
$\Rightarrow\text{T}=1.08\times10^{-1}\ \text{Newton}$
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