Question

A transverse wave propagating on the string can be described by the equation $y=2\sin (10x+300t).$ where $x$ and $y$ are in metres and $t$ in second. If the vibrating string has linear density of $0.6\times {10}^{-3}g/cm$ then the tension in the string is

• A. $5.4N$
• B. $0.054N$
• C. $54N$
• D. $0.0054N$

Answer 1

Answer: (A)

$5.4N$

General equation of progressive wave:

$y=A\sin (\omega t+kx)$

Here, $A$ is amplitude

$\omega$ is angular frequency

$k$is propagation constant

$t$ is time

$x$ is displacement

Given equation:

$y=2\sin (10x+300t).$

Linear charge density, $\mu =0.6\times {10}^{-3}\text{g/cm}\text{=}6\times \text{1}{\text{0}}^{-3}kg{m}^{-1}$

Compare with general equation:

Velocity of the wave in the string:

$v=\frac{\omega }{k}$$=\frac{300}{10}\text{=30}\text{m}{\text{s}}^{-1}$

Relation for velocity in terms of tension:

$T=\mu v^2$$=6\times {10}^{-3}\times {\left(30\right)}^2=5.4N$

Hence, tension in string is$5.4N$