Physics - Sound Wave Question with Solution | TestHub

Fundamental frequency of closed pipe, ${\mathrm{n}}_{\mathrm{c}}=\frac{\mathrm{V}}{4\mathrm{L}}$ Fundamental frequency of open pipe, ${\mathrm{n}}_0=\frac{\mathrm{v}}{2\mathrm{L}}$ They produce 2 beats per second $\begin{array}{rl}& \therefore {\mathrm{n}}_{\mathrm{o}}-{\mathrm{n}}_{\mathrm{c}}=2,\\ & \frac{\mathrm{V}}{2\mathrm{L}}-\frac{\mathrm{V}}{4\mathrm{L}}=2\\ & \frac{\mathrm{V}}{4\mathrm{L}}=2\text{ or }\frac{\mathrm{v}}{\mathrm{L}}=8\end{array}$ When length of open pipe is halved ${\mathrm{n}}_{\mathrm{o}}^{\prime }=\frac{\mathrm{v}}{2\left(\frac{\mathrm{L}}{2}\right)}=\frac{\mathrm{v}}{\mathrm{L}}$ When length of closed pipe is doubled ${\mathrm{n}}_{\mathrm{c}}^{\prime }=\frac{\mathrm{v}}{4\times 2\mathrm{L}}=\frac{\mathrm{v}}{8\mathrm{L}}$ New beat frequency $={\mathrm{n}}_{\mathrm{o}}^{\prime }-{\mathrm{n}}_{\mathrm{c}}^{\prime }=\frac{\mathrm{v}}{\mathrm{L}}-\frac{\mathrm{v}}{8\mathrm{L}}=\frac{7\mathrm{v}}{8\mathrm{L}}=\frac{7}{8}\times 8=7$