question_answer

A cylindrical tube, open at both ends, has a fundamental frequency \[{{f}_{0}}\]in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is:

A)  \[{{f}_{0}}\]

B)  \[3{{f}_{0}}/4\]

C)  \[2{{f}_{0}}\]            

D)  \[{{f}_{0}}/2\]

Correct Answer: A

Solution :

\[{{f}_{0}}=\frac{V}{2l}\]for both end open. Now one end open and one end closed. \[{{f}_{0}}=\frac{V}{4l}\] \[l=l/2\] \[{{f}_{0}}=\frac{V}{4l/2}=\frac{V}{2l}\] \[\therefore \] \[{{f}_{0}}={{f}_{0}}\]