Question

Linear density of a string of is $1.3\times {10}^{-4}kg/m$ and wave equation is $y=0.021sin(x+30t)$. Find the tension in the string where, x in meter and t in second.

• A. 0.12 N
• B. 0.21 N
• C. 1.2 N
• D. 0.012 N

Answer 1

The correct option is A 0.12 N

Given: Linear density of string $m=1.3\times {10}^{-4}kg/m$

Wave equation $y=0.021\sin (x+30t)$

On comparing the given wave equation with $y=a\sin (2\pi x/\lambda +2\pi vt/\lambda )$

We get,

$\lambda =2\pi$

$v=30\lambda /2\pi$

$v=30\times 2\pi /2\pi =30m/s$

Now, velocity of wave in a string of tension $T$ is given by:

$v=\sqrt{T/m}$

$30=\sqrt{T/(1.3\times {10}^{-4})}$

${30}^2=T/(1.3\times {10}^{-4})$

$T=900\times 1.3\times {10}^{-4}=0.12N$