Question

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

• A. $1.17\times {10}^{-2}N$
• B. $1.17\times {10}^{-1}N$
• C. $1.17\times {10}^{-3}N$
• D. None.

Answer 1

The correct option is B $1.17\times {10}^{-1}N$

Velocity of wave = frequency $\times$ wavelength

$\lambda =2\pi$

$\nu =\frac{30}{2\pi }$

$\varphi$ = Linear mass density

velocity = $\frac{30}{2\pi }\times 2\pi =30m/s$

We know,

$v=\sqrt{\frac{T}{\varphi }}$

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

solving this we get

$T=11.7\times {10}^{-2}N$

or

$T=1.17\times {10}^{-1}N$

Hence option (B) is correct.