A Cylindrical Tube, Open At Both Ends, Has A Fundamental Frequency V in Air. The Tube Is Dipped Vertically In Water So That Half Of It Is Inside Water. The Fundamental Frequency Of The Air Column Now Is

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Question

A cylindrical tube, open at both ends, has a fundamental frequency V in air. The tube is dipped vertically in water so that half of it is inside water. The fundamental frequency of the air column now is

Solution

Correct option is

V

 

The frequency of the fundamental mode in an open pipe is given by

                              

And in a closed pipe it is  

                              

Where v is the speed of sound and L is the length of the pipe.

When the tube is dipped in water, L becomes L/2 and V’ becomes

                           

From (i) and (ii) we get V’’ = V.

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