Frequency Equation: Help Finding an Equation Incorporating Tube Diameter

[myshiee]

Hey guys! i was wondering if anyone could help me find an equation to find frequency besides using the formula (velocity= frequency*wavelength).
My teacher said that we needed to find an equation that incorporated the use of the tube's diameter. I've been searching online but I can't find one that uses the diameter. Can anybody help me out?

 

[mukundpa]

Go for "end correction" for standing waves in open or closed tubes.

 

[the_terminator]

For resonance tube experiment:

frequency of tuning fork [n] = velocity of wave / 2*L for tube opened at both ends

frequency [n] = velocity of wave / 4*L for tube opened at one ends.

where L [corrected length] = Resonating length + e [end correction]

where e=0.3 * inner diameter of tube for tube opened at one end

and e=0.6* inner diameter for tube opened at both the ends.

 

[myshiee]

Grazie!

Thanks for the help!
However, I forgot to say that for the open tube, there are two different diameters.Each open side has a different diameter. How would I include that in?