Question

The equation of a wave on a string of linear mass density $0.04kg{m}^{-1}$ is given by $y=0.02\left(m\right)sin\left[2\pi \left(\frac{t}{0.04\left(s\right)}-\frac{x}{0.50\left(m\right)}\right)\right]$ . The tension in the string is

• A. $4.0N$
• B. $12.5N$
• C. $0.25N$
• D. $6.25N$

Answer 1

Answer: (D)

The general equation of wave on string $y=Asin\left[2\pi \left(\frac{t}{T}-\frac{x}{\lambda }\right)\right]$
Wave speed of transverse wave in a stretched string is given by
$v=\sqrt{\frac{T}{\mu }}$
$\Rightarrow T=\mu v^2=\mu \frac{{\left(\omega \right)}^2}{k^2}=0.04\frac{{\left(\frac{2\pi }{0.04}\right)}^2}{{\left(\frac{2\pi }{0.50}\right)}^2}=6.25N$