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(D) For the first resonance,the length of the air column is $L = l + e$,where $l$ is the measured length and $e$ is the end correction.For the first t

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$328$

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(D) For the first resonance,the length of the air column is $L = l + e$,where $l$ is the measured length and $e$ is the end correction.For the first tuning fork: $f_1 = 512\,Hz$,$l_1 = 11\,cm$.The condition for resonance is $L_1 = \frac{\lambda_1}{4} = \frac{v}{4f_1} \Rightarrow 11 + e = \frac{v}{4 	imes 512} \quad (1)$For the second tuning fork: $f_2 = 256\,Hz$,$l_2 = 27\,cm$.The condition for resonance is $L_2 = \frac{\lambda_2}{4} = \frac{v}{4f_2} \Rightarrow 27 + e = \frac{v}{4 	imes 256} \quad (2)$Dividing equation $(1)$ by $(2)$:$\frac{11 + e}{27 + e} = \frac{256}{512} = \frac{1}{2}$$22 + 2e = 27 + e \Rightarrow e = 5\,cm$.Substituting $e = 5$ into equation $(1)$:$11 + 5 = \frac{v}{4 	imes 512} \Rightarrow 16 = \frac{v}{2048}$$v = 16 	imes 2048 = 32768\,cm/s = 327.68\,m/s$.Rounding to the nearest integer,the velocity is $328\,ms^{-1}$.

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