In the resonance experiment,two air columns ( | vedclass

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(D) The fundamental frequency $f$ of an air column closed at one end is given by $f = \frac{v}{4L}$,where $v$ is the velocity of sound and $L$ is the

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$360$

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(D) The fundamental frequency $f$ of an air column closed at one end is given by $f = \frac{v}{4L}$,where $v$ is the velocity of sound and $L$ is the length of the column.For the two columns of lengths $L_1 = 100 \ cm = 1.0 \ m$ and $L_2 = 120 \ cm = 1.2 \ m$,the fundamental frequencies are $f_1 = \frac{v}{4L_1}$ and $f_2 = \frac{v}{4L_2}$.The beat frequency is the difference between these two frequencies: $|f_1 - f_2| = 15 \ Hz$.Substituting the expressions: $\frac{v}{4} \left( \frac{1}{L_1} - \frac{1}{L_2} ight) = 15$.$\frac{v}{4} \left( \frac{1}{1.0} - \frac{1}{1.2} ight) = 15$.$\frac{v}{4} \left( \frac{1.2 - 1.0}{1.2} ight) = 15$.$\frac{v}{4} \left( \frac{0.2}{1.2} ight) = 15$.$\frac{v}{4} \left( \frac{1}{6} ight) = 15$.$v = 15 	imes 4 	imes 6 = 360 \ m/s$.

In the resonance experiment,two air columns (closed at one end) of $100 \ cm$ and $120 \ cm$ long,give $15$ beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is $:$ (in $m/s$)

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