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(B) Let $x$ be the end correction.For the fundamental mode (first resonance),the length of the air column is $l_1 = 0.1 \ m$. The resonance condition

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$0.025$

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(B) Let $x$ be the end correction.For the fundamental mode (first resonance),the length of the air column is $l_1 = 0.1 \ m$. The resonance condition is given by $f = \frac{v}{4(l_1 + x)}$.For the first overtone (second resonance),the length of the air column is $l_2 = 0.35 \ m$. The resonance condition is given by $f = \frac{3v}{4(l_2 + x)}$.Since the same tuning fork is used,the frequency $f$ remains constant. Therefore,$\frac{v}{4(l_1 + x)} = \frac{3v}{4(l_2 + x)}$.Simplifying the equation: $l_2 + x = 3(l_1 + x)$.Substituting the values: $0.35 + x = 3(0.1 + x)$.$0.35 + x = 0.3 + 3x$.$0.05 = 2x$.$x = 0.025 \ m$.

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