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Q.

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 $A B = L / 3$ . Ratio of maximum pressure variation at point A to point B is

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a

$\frac{2}{\sqrt{3}}$

b

$\frac{\sqrt{3}}{2}$

c

$\sqrt{3}$

d

$2$

answer is A.

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Detailed Solution

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$y = 2 A \sin k x \cos ω t, Δ P = 2 (B A K) \cos k x \cos ω t Δ p α \cos k x, \frac{{(Δ p)}_{A}}{{(Δ p)}_{B}} = \frac{\cos k (0)}{\cos k (\frac{L}{3})} = \frac{1}{\cos (\frac{2 π}{λ} . \frac{L}{3})} = \frac{1}{\cos (\frac{2 π}{2 L} . \frac{L}{3})} Δ p = \frac{1}{\cos (\frac{π}{6})} = \frac{2}{\sqrt{3}}$

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