How do you calculate the fundamental frequency of a pipe?

This depends on whether the pipe is closed or open ended.

The fundamental frequency of a pipe is the simplest, smallest portion of a wave that can fit into a pipe. At the open end of a pipe, there is always an antinode - an area with maximum air movement.

If it is an open ended pipe, there is an antinode at each end, meaning that the length of the pipe is equal to 1/2 ##lambda##. Manipulating the formula ##v = f lambda## to solve for the fundamental frequency leaves us with ##f = v / (2L)## in an open ended pipe.

If it is a closed ended pipe, there is an antinode at the open end and a node at the closed end - causing the sound to reflect - meaning that the length of the pipe is equal to 1/4 ##lambda##. Again, if we manipulate the formula ##v = f lambda## to solve for the fundamental frequency, this leaves us with ##f = v / (4L)## in a closed ended pipe.

The website http://www.studyphysics.ca/newnotes/20/unit03_mechanicalwaves/chp141516_waves/lesson51.htm gives further explanation for you.