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A closed organ pipe of length L is vibrating in fundamental frequency. There are two points A and B in the organ pipe as shown, at a distance AB = L / n. Ratio of maximum pressure variation at point A to point B is $\frac{2}{\sqrt{3}} .$ Find the value of n. (Neglect end correction)

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answer is 3.

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Detailed Solution

We have $y = 2 A s i n k x c o s w t$
$| Δ P | = 2 B A K c o s K x c o s w t$
$\frac{{| Δ P |}_{A}}{{| Δ P |}_{B}} = \frac{1}{\cos (π / 2 n)} = \frac{2}{\sqrt{3}}$ hence n=3

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