A long tube open at the top is fixed verticallly and water level inside the tube can be moved up or down . A vibrating tuning fork is held above the open end and the water level is pushed down gradually so as to get first and second resonance at `24.1 cm` and `74.1 cm` , respectively below the open end . The diameter of the tube is

Options

A. `5 cm`
B. `4 cm`
C. `3 cm`
D. `2 cm`

Answer

C

Explanation

`f_(1) = (v)/( 4 ( 24.1 + 0.3 D))`
`f_(3) = ( 3 v)/( 4 (74.1 + 0.3 D))`
`f_(1) = f_(3)`
`rArr = (v)/( 4 ( 24.1 + 0.3 D)) = 3 (v)/( 4 (74.1 + 0.3 D))`
`3 ( 24.1 + 0.3 D) = 74.1 + 0.3 D`
`72.3 + 0.6 D = 74.1 + 0.3 D`
`0.6 D = 74.1 - 72.3`
`0.6 D = 1.8`
`D = (1.8)/(0.6) = 3 cm`