Question

$A$ and $B$ are two metal tubes having equal lengths and equal inner diameters. For the tube $A$, both ends are open while for the tube $B$, one end is closed. What is the ratio of the fundamental frequencies of $A$ and $B$?

• A. $1:2$
• B. $2:1$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is B $2:1$

As tube A is open at both ends so it is an open organ pipe and tube B is closed at one end , it is a closed organ pipe .

Now , fundamental frequency of an open organ pipe (tube A) of length $l$ is given by ,

$n_1=v/2l$ ,

and fundamental frequency of closed organ pipe (tube B) of length $l$ is given by ,

$n_1^{\prime }=v/4l$ ,

therefore ratio of fundamental frequencies ,

$n_1/n_1^{\prime }=2/1$

or $n_1:n_1^{\prime }=2:1$