Experts please solve number 62 and 63
Chapter name WAVE MOTION AND SOUND
Thank you

Dear Student,
63.
$$\begin{gathered} We know time period of the Simple formula is given by- \\ T =2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}} \\ \mathrm{where} \mathrm{T} \mathrm{is} \mathrm{time} \mathrm{period} \\ \mathrm{L} \mathrm{is} \mathrm{the} \mathrm{length} \mathrm{of} \mathrm{the} \mathrm{pendulum} \\ \mathrm{g} \mathrm{is} \mathrm{acceleration} \mathrm{due} \mathrm{to} \mathrm{gravity} \\ we know Frequency, \nu = \frac{1}{T} \\ So, \nu \propto \frac{1}{\sqrt{L}} \\ So , \\ \frac{{\nu }_2}{{\nu }_1}=\sqrt{\frac{L_1}{L_2}} \\ Given , \\ \frac{L_1}{L_2}= \frac{1}{4} \\ So, \\ \frac{{\nu }_2}{{\nu }_1}=\sqrt{ \frac{1}{4}} \\ \frac{{\nu }_1}{{\nu }_2}=\sqrt{ \frac{4}{1}} \\ So their frequecy are in the ratio , \sqrt{4}:1. \end{gathered}$$
​​​​​​Also, we can write it as f₁ : f₂  = 2 : 1

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