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A tuning fork is used to produce resonan...

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of `27 ^(@)C` two successive resonance are produced at 20 cm and 73 cm of column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at `27^(@)` C is

Text Solution

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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`
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