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Q.
A string wave equation is given by $y=0.002 \cos (300 t-15 x)$ and mass density is $\mu=0.1 kg / m$. Then find the tension force in the string.
Waves
Solution:
Given, wave equation, $y=0.002 \cos (300 t-15 x)$
Mass density, $\mu=0.1 kg / m$
Comparing the given wave equation with $y=a \cos (\omega t-k x)$, we have
$\omega=300 rad s ^{-1}, k=15 rad m ^{-1}$
$\therefore$ Velocity of wave,
$v=\frac{\omega}{k}=\frac{300}{15}=20 m / s$
Wave speed in string is also given by
$v=\sqrt{\frac{T}{\mu}}$
where, $T=$ tension in the string and $\mu=$ mass per unit length of string.
Substituting the values in Eq. (i), we get
$20 =\sqrt{\frac{T}{0.1}} \Rightarrow 400=\frac{T}{0.1} $
$\Rightarrow T =40 N$