A tunning fork of frequency 340 Hz is vibrated just above a cylindrical tube. The length of the tube is L = 120 cm. Water is slowly poured into the tube. Determine the minimum height of water required for resonance. ( Take velocity of sound in airv = 340 m//s)

A tunning fork of frequency 340 Hz is vibrated just above a cylindrica

1.	A tunning fork of frequency 340 Hz is vibrated just above a cylindrical tube. The length of the tube is L = 120 cm. Water is slowly poured into the tube. Determine the minimum height of water required for resonance. ( Take velocity of sound in airv = 340 m//s)
Answer» Solution :Here , the tunning fork vibrates in resonance with the air column in the pipe closed at ONE end . The resonant frequency of the air column is GIVEN by ` f = (nv)/( 4l) where n = 1 , 2 , 3 , …` The length of the air column is given by ` l = (nv)/( 4f) = ( n (340))/( 4(340)) = 0.25 nm = 25 ncm` ` l = 25 cm , 75 cm , 125 cm ` Since the length of the tube is `120 cm`, THEREFORE , the POSSIBLE lengths of air column are ` l= 25 cm ` or ` l = 75 cm` If `h` is the height of water filled in the tube , then ` l + h = 120 cm` ` h = 120 - l` For minimum value of `h , l` is maximum , thus `h_(min) = 120 - l_(max) = 120 - 75 = 45 cm`