In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7cm and 83.9cm. Which of the following statements is (are) true?

Let n₁ be the harmonic corresponding to 50.7cm, n₂ the harmonic corresponding to 83.9cm. Since both are consecutive harmonics, their difference = λ/2 ∴ λ/2 = (83.9 – 50.7)cm λ/2 = 33.2cm λ = 66.4cm λ/4 = 16.6cm
Length corresponding to fundamental mode must be close to λ/4. 50.7cm must be closed to an odd multiple of this length as 16.6 × 3 = 49.8cm. therefore 50.7 is 3rd harmonic
e + 50.7 = 3λ/4 e = 49.8 – 50.7 = -0.9cm
Speed of sound, v = fλ ∴v = 500 × 66.4cm/sec = 332.000m/s.
Hence, Option (A), (B) and (C) are correct