An air column in a pipe which is closed at one end will be in resonance with a vibrating tuning fork of frequency 415 Hz for various vibrating air columns. Which one of the following lengths is not in resonance ? (velocity of sound in air = 332 m/s) (Neglect end correction)

Step-by-step solution

Given frequency f = 415 Hz and velocity v = 332 m/s . The wavelength of the sound wave is: = v f = 332 415 m = 0.8 m = 80 cm For a pipe closed at one end, the resonating lengths are given by odd multiples of 4 : L = (2n - 1) 4 where n = 1, 2, 3, The possible resonating lengths are: L₁ = 1 80 4 = 20 cm L₂ = 3 80 4 = 60 cm L₃ = 5 80 4 = 100 cm Among the given options, 40 cm is an even multiple of 4 and therefore is not a resonating length.