A tuning fork of frequency 340 Hz is vibrated just above a tube of 120 cm height. Water is slowly poured in the tube. What is the minimum height of water necessary for resonance?

Step-by-step solution

Because the tuning fork is in resonance with air column with a pipe closed at one end, the frequency is n = (2 ~N -1) v 4 l where N =1,2,3 . corresponds to different modes of vibration Substituting n =340 ~Hz , v =340 ~m / s (speed of sound in air), the length of air column in the pipe can be l= (2 ~N -1) 340 4 340 = (2 ~N -1) 4 ~m = (2 ~N -1) 100 4 ~cm For N =1,2,3, we get l=25 ~cm , 75 ~cm , 125 ~cm . . . etc. As the tube is only 120 cm long, length of air column after water is poured in it may be 25 cm or 75 cm