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

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answer is 3.

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Detailed Solution

$(3) y = 2 A \sin k x \cos ω t$

$|Δ P| = 2 B A k \cos k x \cos ω t$

There will be a phase difference of $\frac{π}{2}$ for the length of L,

So the phase difference for length of $\frac{L}{n}$ is given by $\frac{π}{2 n}$

It is given that $\frac{{|Δ P|}_{A}}{{|Δ P|}_{B}} = \frac{1}{\cos \frac{π}{2 n}} = \frac{2}{\sqrt{3}}$

$\Rightarrow n = 3$

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