An open pipe 0.400 m in length is placed vertically in a cylindrical bucket and nearly touches the bottom of the bucket, which has an area of 0.100 m2. Water is slowly poured into the bucket until a sounding tuning fork of frequency 440 Hz, held over the pipe, produces resonance. Find the mass of water in the bucket at this moment. Take velocity of sound in air as 330 m/s.

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Question

An open pipe 0.400 m in length is placed vertically in a cylindrical bucket and nearly touches the bottom of the bucket, which has an area of 0.100 m². Water is slowly poured into the bucket until a sounding tuning fork of frequency 440 Hz, held over the pipe, produces resonance. Find the mass of water in the bucket at this moment. Take velocity of sound in air as 330 m/s.

18.75 kg

40.00 kg

21.25 kg

26.75 kg

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$ℓ = (2n + 1) \frac{λ}{4}$

$λ = \frac{330}{440} = 0.75$

$ℓ = (2n + 1) \times \frac{3}{16} = 0.1875 (2n + 1)$

ℓmin = 0.1875 m

h = 0.4 – 0.1875 = 0.2125 m

m = 0.2125 × 0.1 × 10³ = 21.25 kg