Two vibrating modes of an air column are shown in figure. What is the ratio of frequency of two notes ?

Explanation

In mode (a),
`l=lambda//2+lambda//4=3lambda//4, lambda=(4l)/(3)`
`n_(1)=(upsilon)/(lambda)=(3upsilon)/(4l)`
In mode (b),
`l=lambda//2+lambda//2+(lambda)/(4)=(5lambda)/(4), lambda=(4l)/(5)`
`n_(2)=(upsilon)/(lambda)=(5upsilon)/(4l) :. (n_(1))/(n_(2))=(3)/(5)`