Confused about string instruments and standing waves

[bt1740]

So I made a banjo for my project and now I need to do the calculations.
Well since its a string instrument I have to find the frequencies of the first four harmonics, I already have the fundamental frequency.
Is it fine to use:
fn = nf1

Not sure because I thought that was for open end air columns?

 

[Simon Bridge]

Welcome to PF;
Do not go by equations you find in a book - go by the physics.
You know that the fundamental and all harmonics must form sine waves - you should be able to sketch a sine wave.

Your banjo has strings - is the string attached at both ends or just one?
The attached ends of the string must remain still - so the amplitude there is zero: they are nodes.
You get an antinode (max amplitude) between every two nodes.
Each harmonic up adds a node.

So sketch out the possible sine wave for 2 nodes, then for three nodes, and so on until you see a pattern.