In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 H z 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 c m a n d 83.9 c m . Which of the following statements is (are) true?

Step-by-step solution

Let n 1 harmonic is corresponding to 50.7   c m   a n d     n 2 harmonic is corresponding 83.9   c m . since both one consecutive harmonics. ∴   There difference = λ 2 ∴   λ 2 = 83.9 - 50.7 c m λ 2 = 33.2   c m λ = 66.4   c m ∴   λ 4 = 16.6 c m length corresponding to fundamental mode must be close to λ 4   a n d   50.7   c m must be an odd multiple of this length 16.6   ×   3   = &#1