Question

an open and closed organ pipe have same length. the ratio of Pth mode of frequency of air in two pipes is?

Answer 1

Dear Student,

$$\begin{gathered} {\mathrm{p}}^{\mathrm{th}}\mathrm{mode}\mathrm{of}\mathrm{vibration}\mathrm{of}\mathrm{open}\mathrm{organ}\mathrm{pipe}{\mathrm{n}}_1=\mathrm{p}\times \frac{\mathrm{v}}{2\mathrm{l}} \\ {\mathrm{p}}^{\mathrm{th}}\mathrm{mode}\mathrm{of}\mathrm{vibration}\mathrm{of}\mathrm{closed}\mathrm{organ}\mathrm{pipe}{\mathrm{n}}_2=\frac{\left(2\mathrm{p}-1\right)}{2}\times \frac{\mathrm{v}}{2\mathrm{l}} \\ \frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}=\frac{\mathrm{p}\times \frac{\mathrm{v}}{2\mathrm{l}}}{\frac{\left(2\mathrm{p}-1\right)}{2}\times \frac{\mathrm{v}}{2\mathrm{l}}} \\ \frac{{\mathrm{n}}_1}{{\mathrm{n}}_2}=\frac{2\mathrm{p}}{2\mathrm{p}-1} \end{gathered}$$