Question

In an experment 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? 

(A) The speed of sound determined from this experiment is 332ms^–1 

(B) The end correction in this experiment is 0.9cm 

(C) The wavelength of the sound wave is 66.4cm 

(D) The resonance at 50.7cm corresponds to the fundamental harmonic

Answer 1

Let n₁ harmonic is corresponding to 50.7cm & n₂ harmonic is corresponding 83.9cm. since both one consecutive harmonics.

∴ their difference = λ/2

∴ λ/2 = (83.9 - 50.7)cm

length corresponding to fundamental mode must be close to λ/4 & 50.7cm must be an odd multiple of this length 16.6 × 3 = 49.8cm. therefore 50.7 is 3^rd harmonic
If end correction is e, then