In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency $500 Hz$ 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 $50.7 cm$ and $83.9 cm$. Which of the following statements is (are) true?
$(A)$ The speed of sound determined from this experiment is $332 m s ^{-1}$
$(B)$ The end correction in this experiment is $0.9 cm$
$(C)$ The wavelength of the sound wave is $66.4 cm$
$(D)$ The resonance at $50.7 cm$ corresponds to the fundamental harmonic
IIT 2018, Diffcult
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