Question

The equation of a wave on a string of linear mass density $0.04kgm^{- 1}$ 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. $4.0 \, N$
• B. $12.5N$
• C. $0.25 \, N$
• D. $6.25 \, N$

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
$v=\sqrt{\frac{T}{\mu }}$
$\Rightarrow T=\mu v^{2}=\mu \frac{\left(\omega \right)^{2}}{k^{2}}=0.04\frac{\left(\frac{2 \pi }{0 .04}\right)^{2}}{\left(\frac{2 \pi }{0 .50}\right)^{2}}=6.25N$