How does the diameter of an open ended tube affect the frequency? I measured (using a software) the fundamental frequency produced in an open ended tube of different lengths. Does the diameter of an open ended (both ends) tube affect the fundamental frequency?
 A: 
The formula you derive for the resonance frequency of an organ pipe won't have a radius variable in the formula. The resonance frequency depends only on the length of the organ pipe. Theoretically, it is correct. 
For practical purposes, this is strictly not true. The frequency measured always tends to be lower than what you theoretically calculate. The pipe appears to be acoustically somewhat longer than its physical length. The increase in length depends on the radius of the pipe.
To account for that, additional corrective length (approximate) is added in the formula.
$$\Delta L_{closed-pipe} = 0.6r = 0.3D$$
$$\Delta L_{open-pipe} = 1.2r = 0.6D$$
The cause of this increase in length is:

A theoretical basis for computation of the end correction is the
  radiation acoustic impedance of a circular piston. This impedance
  represents the ratio of acoustic pressure at the piston, divided by
  the flow rate induced by it. The air speed is typically assumed to be
  uniform across the tube end. This is a good approximation, but not
  exactly true in reality, since air viscosity reduces the flow rate in
  the boundary layer very close to the tube surface. Thus, air column
  inside the tube is loaded by the external fluid due to sound energy
  radiation. This requires an additional length to be added to the
  regular length for calculating the natural frequency of the pipe
  system.
  Source: https://en.wikipedia.org/wiki/End_correction

