Two organ pipes of same length, open at both ends produce sound of different pitch, if their radii are different. Why?

Explanation

The fundamental frequency of an open organ pipe is given by
`v = (upsilon)/(2 (L + 0.3 D))`
where D is the diameter of the pipe and 0.3 D is the end correction. Clearly, even if the lengths of the pipes are same but their radii are different, sounds of different frequencies will be produced by them.