A cylindrical tube, open at both ends, has a fundamental frequency `f` in air . The tube is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now
(a) `f // 2`
(b) `3 f // 4`
(C ) `f`
(d) `2f`

Options

A. f/2
B. f
C. 3f/4
D. 2f

Answer

B

Explanation

Frequency of open organ pipe
` f _ ("open") = (v ) /(2 I _ ( "open")) `
Similarly frequency of closed organ pipe
` f_("closed") = ( v ) /( 4l _ ( "closed")) = (v) /( 4l _ ( "open") l 2 ) = ( v ) /(2 f _ ( "open")) `
` = f _ ("open") = f As, l _ ( "closed") = ( l _ ("open")/(2) ) `
i.e. frequency remains unchanged.