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Question:

A resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to:

328ms𕒵

322ms𕒵

341ms𕒵

335ms𕒵

Solution:

λ₁/4 = 11cm
so, v512 × 4 = 11cm ___(1)
λ₂/4 = 27cm
so, v256 × 4 = 27cm ___(2)
(2) - (1)
v256 × 4 - v512 × 4 = 27cm - 11cm
4(v256 - v512) = 16cm
Since frequency is half, wavelength is double.
So, λ₂ = 2λ₁
Therefore, v256 × 4 × 0.5 = 0.16m
v = 0.16 × 2 × 4 × 256
v = 327.68 m/s ≈ 328 m/s