While measuring the speed of sound by performing a resonance column experiment, a student gets the f

Question

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be $x \mathrm{~cm}$ for the second resonance. Then\

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(c) : $v_{1}=\sqrt{\frac{\gamma R T}{M}}$ assuming $M$ is the average molar mass of the air (i.e., nitrogen) and $\gamma$ is also for nitrogen.\ $v_{1}=\sqrt{\frac{\gamma R T_{1}}{M}} ; v_{2}=\sqrt{\frac{\gamma R T_{2}}{M}}$\ where $T_{1}$ and $T_{2}$ stand for winter and summer temperatures.\ $1^{	ext {st }}$ resonance\ $L_{1}=\frac{
u_{1}}{n}=\frac{\lambda}{4}=18 \mathrm{~cm}$\ at temperature $T_{1}$.\ At $T_{2}$, summer, $v_{2}>v_{1}$.\ $L_{2}=\frac{v_{2}}{n}=\frac{3 \lambda}{4}>3 	imes 18 . 	herefore L_{2}>54 \mathrm{~cm}$\ or $\quad x>54 \mathrm{~cm}$.\