(હવામાં ધ્વનિની ઝડપ $= 340\, m/s$)
or \(\lambda=\frac{\mathrm{v}}{\mathrm{v}}=\frac{340 \mathrm{m} / \mathrm{s}}{340 \mathrm{Hz}}=1 \mathrm{m}\)
First resonating length,
\(l_{1}=\frac{\lambda}{4}=\frac{1}{4} \mathrm{m}=25 \mathrm{cm}\)
second resonating length,
\(l_{2}=\frac{3 \lambda}{4}=\frac{3 \times 1 \mathrm{m}}{4}=75 \mathrm{cm}\)
Third resonating length,
\(l_{3}=\frac{5 \lambda}{4}=\frac{5 \times 1 \mathrm{m}}{4}=125 \mathrm{cm}\)
So third resonance is not possible since the length of the tube is \(120 \mathrm{cm}\).
Minimum height of water necessary for resonance \(=120-75=45 \mathrm{cm}\)
${y}_{1}={A}_{1} \sin {k}({x}-v {t}), {y}_{2}={A}_{2} \sin {k}\left({x}-{vt}+{x}_{0}\right)$
કંપવિસ્તાર ${A}_{1}=12\, {mm}$ અને ${A}_{2}=5\, {mm}$ ${x}_{0}=3.5\, {cm}$ અને તરંગ સદીશ ${k}=6.28\, {cm}^{-1}$ આપેલ છે.
તો પરીણામી તરંગનો કંપવિસ્તાર $......\,{mm}$ થશે.