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 leavel 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?

Options

A. The speed of sound determined from this experiment is 332 `ms^(-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

Answer

A, C

Explanation

`(2n + 1) (lambda)/(4) = 50.7 + e" "...(i)`
`(2n + 3) (lambda)/(4) = 83.9 + e" "...(ii)`
Here e is end correction.
Subtracting equation (i) from equation (ii), we get the following :
`(lambda)/(2) = 33.2 rArr = 66.4` cm (Option (c) is correct.)
`upsilon = f lambda = 500 xx 0.664 = 332` m/s (Option (a) is correct)
If we use n = 1, then e = -0.9
We cannot say that first resonance is corresponding to fundamental mode.