Question

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

• A. $10$
• B. $0.5$
• C. $1$
• D. $0.11$

Answer 1

The correct option is D $0.11$

The equation for the transverse vibrations is:

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

The wave speed is given by:

$\Rightarrow v=\frac{\omega }{k}=\frac{30}{1}=30m/s$

using, $v=\sqrt{\frac{T}{m}}$, the tension can be obtained as:

$\Rightarrow 30=\sqrt{\frac{T}{1.3\times {10}^{-4}}}$

$\Rightarrow T=0.11N$