Physics - Wave on String Question with Solution | TestHub

Given, Tension in the string, $\mathrm{T}=0.25\mathrm{N}$ a mass per unit length, $\mu =1\mathrm{mg}/\mathrm{m}=10^{-6}\mathrm{kg}/\mathrm{m}$ Velocity of wave, $v=\sqrt{\frac{T}{H}}\dots (i)$ The distance between two consecutive nodes is equal to half the wave length ' $\lambda$ '. $\therefore v=f\lambda \dots (ii)$ Form Eqs. (i) and (ii), $\begin{array}{rl}\mathrm{f}\lambda =\sqrt{\frac{\mathrm{T}}{\mathrm{m}}}\Rightarrow \lambda & =\frac{1}{\mathrm{f}}\sqrt{\frac{\mathrm{T}}{\mu }}=\frac{1}{250}\sqrt{\frac{0.25}{10^{-6}}}\\ \lambda & =2\end{array}$ $\therefore$ Difference between two consecutive nodes $=\frac{\lambda }{2}=\frac{2}{2}=1\mathrm{m}$