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In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of $2\ 	ext{cm}^2$, the amount of water poured in the organ tube is ______ g. (Take speed of sound in air is 330 m/s) A). 200 B). 400 C). 300 D). 100

Edvaya · Accepted Answer

The correct answer is 400. For a closed organ pipe: $f = \dfrac{v}{4L}$
Initial length: $L_1 = \dfrac{v}{4f_1} = \dfrac{330}{4 	imes 30} = 2.75\ 	ext{m}$
Final length (with water): $L_2 = \dfrac{v}{4f_2} = \dfrac{330}{4 	imes 110} = 0.75\ 	ext{m}$
Height of water column: $h = L_1 - L_2 = 2.75 - 0.75 = 2.0\ 	ext{m} = 200\ 	ext{cm}$
Volume of water: $V = A 	imes h = 2\ 	ext{cm}^2 	imes 200\ 	ext{cm} = 400\ 	ext{cm}^3$
Mass of water: $m = ho V = 1\ 	ext{g/cm}^3 	imes 400\ 	ext{cm}^3 = 400\ 	ext{g}$

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