Question

A transverse wave described by an equation y = 0.02 sin (x + 30t) where x and t are in meter and second, is traveling along a wire of area of cross-section $1m{m}^2$ and density $8000k{g}^{-3}$. What is the tension in the string?

• A. 20 N
• B. 7.2 N
• C. 30 N
• D. 14.4 N

Answer 1

The correct option is B 7.2 N

Equation of wave is given by:
$y=Asin(kx-\omega t)$
Comparing this with the given equation, we get:
$k=1,\omega =30$
Wave velocity = $\frac{\omega }{k}=30m{s}^{-1}$
Wave velocity is also given by the relation $v=\sqrt{\frac{T}{\mu }}$
Given that $\mu =\frac{m}{L}=\rho A=8000\ast {10}^{-6}=8\ast {10}^{-3}{m}^2$
i.e.
$30=\sqrt{\frac{T}{8\ast {10}^{-3}}}$
$900=\frac{T}{8\ast {10}^{-3}}$
$T=7.2N$
Option B is correct.