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 83.9 cm. Which of the following statements is (are) true?

let n1  harmonic is corresponding to 50.7 cm &  n2 harmonic is corresponding 83.9 cm.∴ λ2=(83.9−50.7) cm                                       ⇒λ2=33.2 cm⇒λ=66.4 cm ∴Option (3) is correct                                      ∴Fundamental frequency= λ4=16.6 cm ∴Option (4) is incorrectLength corresponding to fundamental mode must be close to  λ4 & 50.7 cm must be an odd multiple of this length 16.6×3=49.8cm. therefore 50.7 is  3rd harmonic If end correction is e, thene+50.7=3λ4⇒e=-0.9cm End correction can never be negative ∴option(2) is incorrectSpeed of sound,  v=fλ∴ v=500×66.4  cm/sec =332.000 m/s ∴Option (1) is correcttherefore options (1), (3) are correct