A string wave equation is given $y=0.002 \sin (300 t-15 x)$ and mass density is $\mu=\frac{0.1\, kg }{m}$. Then find the tension in the string, (in $N$)
AIIMS 2019, Medium
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The given string wave equation is,
$y=0.002 \sin (300 t-15 x)$
From the above equation,
$\omega=300$
$k=15$
The wave speed is calculated as,
$v=\frac{\omega}{k}$
$=\frac{300}{15}$
$=20 m / s$
Also, the expression for the wave speed in the string is,
$v=\sqrt{\frac{T}{\mu}}$
$20=\sqrt{\frac{T}{0.1}}$
$T=0.1 \times 20^{2}$
$=40 N$
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