Question

286.In the experiment for determination of the speed of sound in air using resonance tube method.The length of air column that resonates with fundamental mode with a tuning fork is 0.1m.When its length is changed to 0.35m it resonates in first overtone.The end correction is

Answer 1

Dear Student,

$$\begin{gathered} {\mathrm{l}}_1+0.3\mathrm{d}=\frac{\mathrm{\lambda }}{4}...............\left(1\right) \\ {\mathrm{l}}_2+0.3\mathrm{d}=\frac{3\mathrm{\lambda }}{4}................\left(2\right) \\ {\mathrm{l}}_2-{\mathrm{l}}_1=\frac{3\mathrm{\lambda }}{4}-\frac{\mathrm{\lambda }}{4} \\ {\mathrm{l}}_2-{\mathrm{l}}_1=\frac{3\mathrm{\lambda }-\mathrm{\lambda }}{4} \\ {\mathrm{l}}_2-{\mathrm{l}}_1=\frac{2\mathrm{\lambda }}{4} \\ {\mathrm{l}}_2-{\mathrm{l}}_1=\frac{\mathrm{\lambda }}{2} \\ 0.35-0.1=\frac{\mathrm{\lambda }}{2} \\ 0.25=\frac{\mathrm{\lambda }}{2} \\ \mathrm{divide}\mathrm{by}2\mathrm{both}\mathrm{side}, \\ \frac{0.25}{2}=\frac{\frac{\mathrm{\lambda }}{2}}{2} \\ 0.125\mathrm{m}=\frac{\mathrm{\lambda }}{4} \\ \mathrm{Substitute}\mathrm{it}\mathrm{in}\mathrm{equation}\left(1\right), \\ {\mathrm{l}}_1+0.3\mathrm{d}=0.125 \\ 0.3\mathrm{d}=0.125-0.1 \\ 0.3\mathrm{d}=0.025\mathrm{m} \end{gathered}$$