A cylinderical 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

Options

A. `f_(0)`
B. `3f_(0)//4`
C. `2f_(0)`
D. `f_(0)//2`

Answer

A

Explanation

Let the length of the open pipe be l cm.
`therefore`Fundamental frequency, `f_(o)=v//2l,` where v is the velocity of sound. When half of the length of the tube is filled with water by dipping it vertically in water, it will be a closed pipe having length of `l//2`.
`therefore`fundamental frequency of closed pipe.
`f_(o).=(v)/(4xx(l//2))=(v)/(2l)=f_(o)`.