Question

The linear density of a vibrating string is ${10}^{-4}kg/m$. A transverse wave is propagating on the string, which is described by the equation y = 0.02 sin (x + 30 t), where x and y are in meters and time t in seconds. Then tension in the string is

• A. 0.09 N
• B. 0.36 N
• C. 0.9 N
• D. 3.6 N

Answer 1

The correct option is A

0.09 N

y = 0.02 sin (x+30t)

Comparing with standard equation

$y=Asin(Kx+\omega t),\omega =30,K=1$

Velocity of wave,

$v=\frac{\omega }{K}=\frac{30}{1}=30m/sExpressionv=\sqrt{\frac{T}{\mu }}givesTensionT=v^2\mu =(30{)}^2\times {10}^{-4}=0.09N$