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  4. A string has a mass per unit length 5gm/m . Equation of a travelling wave on this stretched string is y=0.03sin (.450t-9x.) , where distance and time are measured in SI units. The tension in the string will be ?

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Q. A string has a mass per unit length $5gm/m$ . Equation of a travelling wave on this stretched string is $y=0.03sin$ $\left(\right.450t-9x\left.\right)$ , where distance and time are measured in SI units. The tension in the string will be ?

NTA AbhyasNTA Abhyas 2020

Solution:

$k=9\omega =450$
$\therefore v=\frac{\omega }{k}=50m/s$
$v=\sqrt{\frac{T}{\mu }}$
$\therefore T=μv^{2}=50^{2}\times 5\times 10^{- 3}=12.5N$