Question

A tube closed at one end and containing air, produces, when excited, the fundamental note of frequency $512Hz$. If the tube is open at both ends, the fundamental frequency that can be excited is (in $Hz$) :

• A. 1024
• B. 512
• C. 256
• D. 128

Answer 1

The correct option is A 1024

Fundamental frequency of closed organ pipe (tube closed at one end) is given by ,

$n_1=v/4l$ , .....................eq1

where $v=$ velocity of wave ,

$l=$ length of the closed tube ,

and fundamental frequency of open organ pipe (tube opened at both ends) is given by ,

$n_1^{\prime }=v/2l$ , ......................eq2 ,

dividing eq2 by eq1 ,

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

or $n_1^{\prime }=2n_1=2\times 512=1024Hz$ , (given , $n_1=512Hz$)