JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Waves & Sound

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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 cm², the amount of water poured in the organ tube is ______ g. (Take speed of sound in air is 330 m/s)

Answer: 400

Solution

Closed pipe:

f = \frac{v}{4 ℓ}

. Initial length

ℓ_{1} = \frac{330}{4 ( 30 )} = 2.75 m

; after water is poured in,

ℓ_{2} = \frac{330}{4 ( 110 )} = 0.75 m

.

The air column shortens by

Δ ℓ = 2 m

, which is filled by water.

Volume

= A Δ ℓ = 2 c m^{2} \times 200 cm = 400 c m^{3}

, and with

ρ = 1 g/c m^{3}

, mass

= 400 g

JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Integer answer

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