For the tube open at one the resoN/Asnce frequencies are `(nv)/(4l)` when n is a positive odd interger. If the tuning fork has a frequency v and `l_1, l_2, l_3` are the successive lengths of the tube in resoN/Ance with it, we have
`(nv)/(4l_1)=v`
`((n+2)v)/(4l_2)=v`
`(n+4)v)/(4l_3)=v`
`giving l_3-l_2=l_2-l_1=(2v)/(4v)=v/(2v)`
By the question l_3-l_2=(52.75-31.25)cm=21.50cm` and `l_2-l_1=(31.25-9.75)m=21.50cm`.
`Thus, v/(2v)=21.50cm`
`or v=2vxx21.50cm=2xx800s^-1xx21.50cm=344ms^-1`