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  4. Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t - 9x) where distance and time are measured is SI units. The tension in the string is :

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Q. Equation of travelling wave on a stretched string of linear density $5\, g/m$ is $y\, =\, 0.03\, sin(450\, t - 9x)$ where distance and time are measured is SI units. The tension in the string is :

JEE MainJEE Main 2019Waves

Solution:

$y =0.03 \sin\left(450 t - 9x\right) $
$ v= \frac{\omega}{k} =\frac{450}{9} =50 m/s $
$v= \sqrt{\frac{T}{\mu}} \Rightarrow \frac{T}{\mu} =2500 $
$ \Rightarrow T = 2500 \times5 \times10^{-3} $
$ = 12.5 \,N $