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A resonance tube is old and has jagged end. It is still used in the laboratory to determine 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 the 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. If the velocity of sound in air, obtained in the experiment, is close to:

1. 335 m s⁻¹
2. 328 m s⁻¹
3. 341 m s⁻¹
4. 322 m s⁻¹

Correct answer: 328 m s⁻¹

Solution

With unknown end correction e: L1+e=v/(4*512), L2+e=v/(4*256). Subtracting, L2-L1=0.16 m = v/2048, giving v=0.16*2048 = 328 m/s.

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