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(C) In a resonance tube experiment,the resonance lengths $l_1$ and $l_2$ are related to the wavelength $\lambda$ and end correction $e$ as follows:$l_

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(C) In a resonance tube experiment,the resonance lengths $l_1$ and $l_2$ are related to the wavelength $\lambda$ and end correction $e$ as follows:$l_1 + e = \frac{\lambda}{4}$$l_2 + e = \frac{3\lambda}{4}$Dividing the second equation by the first,we get:$\frac{l_2 + e}{l_1 + e} = 3$$l_2 + e = 3(l_1 + e)$$l_2 + e = 3l_1 + 3e$$l_2 - 3l_1 = 2e$$e = \frac{l_2 - 3l_1}{2}$Given $l_1 = 12 ~cm$ and $l_2 = 38 ~cm$:$e = \frac{38 - 3(12)}{2} = \frac{38 - 36}{2} = \frac{2}{2} = 1 ~cm$.

In a resonance tube experiment,a tuning fork resonates with an air column of length $12 ~cm$ and again resonates when the air column is $38 ~cm$ long. The end correction will be: (in $~cm$)

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