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In an organ pipe (which may be closed or open) of 99 cm length, standing wave is set up whose equation is given by longitudinal displacement. x = 0.3 (mm) cos $[(2 π / 0.8) (z + 0.01 m)]$ cos 400 t, where z is measured form the top of tube in metres and t is in seconds. Take end correction = 1 cm. Choose the CORRECT statements.

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The upper end and lower end of tube are closed and open respectively

The air column is vibrating in third harmonic

The upper end and lower end of tube are open and closed respectively

The air column is vibrating in second overtone

answer is A, D.

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Detailed Solution

As there is antinode at z=-0.01 m, the open end is at the top of the organ pipe.

$\begin{array}{l} \frac{2 π}{λ} = K = \frac{2 π}{0.8} \\ λ = 0.8 m \\ \frac{λ}{4} = 20 cm \\ ℓ + e = 100 cm = \frac{5 λ}{u} \end{array}$

hence second over tone closed organ pipe.

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