Question

In a resonance-column experiment, a long tube, open at the top, is clamped vertically. By a separate device, water level inside the tube can be moved up or down. The section of the tube from the open end to the water level act as closed organ pipe. A vibrating tuning fork is held above the open end, first and the second resonances occur when the water level is 24.1 cm and 74.1 cm repsectively below the open end. Find the diameter of the tube. [Hint : end correction is 0.3 d]

• A. $3cm$
• B. $6cm$
• C. $9cm$
• D. $12cm$

Answer 1

The correct option is A $3cm$

We have , end correction in a resonance tube is ,

$e=\frac{l_2-3l_1}{2}$ ,

given $l_1=24.1cm,l_2=74.1cm$ and $e=0.3d$ , (d=diameter of tube ) ,

therefore , $0.3d=\frac{74.1-3\times 24.1}{2}$ ,

or $0.3d=\frac{1.8}{2}=0.9$ ,

or $d=0.9/0.3=3cm$