A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is

Options

A. `1:2`
B. `2:1`
C. `2:3`
D. `4:3`

Answer

A

Explanation

Avoiding and correction, the length of close organ pipe is
`l_(2)=(lambda_(1))/4` or `lambda_(1)=4l_(1)`
The length of open organ pipe is
`l_(2)=(lambda_(2))/2` or `lambda_(2)=2l_(2)`
Here, `n_(1)=n_(2)`
`rArr (v_(1))/(lambda_(1))=v/(lambda_(2))`
or `v/(4l_(1))=v/(4l_(2))`
Therefore `l_(1):l_(2)=1:2`