Physics - Sound Wave Question with Solution | TestHub

First resonance will occure at $l_1+\mathrm{x}=\frac{\lambda }{4}$ Second resonance will occure at $l_2+\mathrm{x}=\frac{3\lambda }{4}$ Second resonance will occure at $l_2+\mathrm{x}=\frac{3\lambda }{4}$ $$\begin{array}{rl}& l_2+\mathrm{x}=3\left(l_1+\mathrm{x}\right)\\ & l_2+\mathrm{x}=3l_1+3\mathrm{x}\\ & 2\mathrm{x}=l_2-3l_1\\ & \therefore \mathrm{x}=\frac{l_2-3l_1}{2}\\ & =\frac{70.2-68.1}{2}=1.05\mathrm{cm}\end{array}$$ $\therefore$ Third resonance occurs at $l_3+\mathrm{x}=\frac{5\lambda }{4}$ $$\begin{array}{rl}\therefore l_3& =5\left(l_1+\mathrm{x}\right)-\mathrm{x}\\ & =5l_1+4\mathrm{x}\\ & =113.5+4.2\\ & =117.7\mathrm{cm}\end{array}$$