Physics - Sound Wave Question with Solution | TestHub

(A) Frequency of vibration $\mathrm{n}=\frac{1}{2\mathrm{e}}\sqrt{\frac{\mathrm{T}}{\mathrm{m}}}$ If $\mathrm{T}=\mathrm{Mg}$, then $\mathrm{n}=\frac{1}{2\mathrm{e}}\sqrt{\frac{\mathrm{Mg}}{\mathrm{m}}}$ If ${\ell }_1$ and ${\mathrm{g}}_1$ are length and acceleration due to gravity at the pole and ${\ell }_2$ and ${\mathrm{g}}_2$ at the equator then, if frequency is same, then $n=\frac{1}{2{\ell }_1}\sqrt{\frac{M{g}_1}{m}}=\frac{1}{2{\ell }_2}\sqrt{\frac{M{g}_2}{m}}$ $\therefore \frac{\sqrt{g_1}}{{\ell }_1}=\frac{\sqrt{g_2}}{{\ell }_2}$ or $\frac{{\ell }_2}{{\ell }_1}=\sqrt{\frac{g_2}{g_1}}$ ${\mathrm{g}}_2<{\mathrm{g}}_1\therefore {\ell }_2<{\ell }_1$