1. Tardigrade
  2. Question
  3. Physics
  4. A string is producing transverse vibration whose equation is y=0.021 sin (x+30 t), Where x and y are in meters and t is in seconds. If the linear density of the string is 1.3 × 10-4 kg / m, then the tension in the string in N will be :

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Q. A string is producing transverse vibration whose equation is $y=0.021 \sin (x+30 t)$, Where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times 10^{-4} kg / m$, then the tension in the string in $N$ will be :

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Solution:

We use
$y=0.021 \sin (x+30 t)$
Wave speed is given as
$v=\frac{\omega}{k}=\frac{30}{1}=30\, m / s$
Using, $v=\sqrt{\frac{T}{m}}$
$\Rightarrow 30=\sqrt{\frac{T}{1.3 \times 10^{-4}}}$
$\Rightarrow T=0.117\, N.$