Question

A pipe of length $L$ and open at both ends produced a note of fundamental frequency $f_1$. When the pipe is kept with $3/4$ of its length in water, it produces a note of fundamental frequency $f_2$. the ratio $f_2/f_1$ is:

• A. $1:1$
• B. $1:2$
• C. $2:1$
• D. $3:2$

Answer 1

The correct option is C $2:1$

Initially the pipe of length $L$ is open at both ends , so it is an open organ pipe and fundamental frequency $f_1$ of an open pipe is given by ,

$f_1=v/2L$ ,

now pipe is dipped in water with $3/4$ of its length in water , therefore it is now a closed organ pipe , having an air column of length $L^{\prime }$ ,

and $L^{\prime }=L-3L/4=L/4$ .

fundamental frequency $f_2$of a closed pipe of length $L^{\prime }$ is given by ,

$f_2=v/4L^{\prime }=v/4\left(L/4\right)=v/L$ , (because $L^{\prime }=L/4$) ,

dividing $f_2$ by $f_1$ , we get

$f_2/f_1=2/1$ ,

or $f_2:f_1=2:1$