A source of frequency 340 Hz is kept above a vertical cylindrical tube closed at lower end. The length of the tube is 120 cm. Water is slowly poured in just enough to produce resonance. Then, the minimum height (velocity of sound = 340 m/s) of the water level in the tube for that resonance is

Explanation

`f=n(v)/(4L)` with n=1,3,5
So length of air column in the pipe
`L=(nv)/(4f)=25` n cm with n=,1,3,5...
i.e, `L=25 cm 75 cm , 125 cm`
Low as the tube is 120 cm, so length of air column must be lesser than 120 cm, i.e., it can be only 25 cm or 75 cm. Further if h is the height of water filled in the tube, `L+h=120 cm or h=120-L`
So h will be minimuim when `L_(max)=75 cm`
`:.(h)_(min)=120-75=45 cm`