The fundamental frequency of the pipe is the simplest, smallest portion of the wave that can fit into a pipe.

Open-end pipe:

At an open-end of a pipe, there is an anti node. There is an area of maximum air movement at the open end of a pipe.

For open organ pipe fundamental node, L₀ = λ₀ / 2 ; λ₀ = 2L₀ ; We know f = v/λ, Hence, f₀ = v / λ₀ = v / 2L₀  ------Eqn (1)

Close ended pipe:

At a close ended of a pipe, there is an anti node at the open end and a node at the closed end causing sound to reflect. There is an area of maximum air movement at the open end of a pipe.

For close ended organ pipe fundamental node, L₀ = λ₀ / 4 ; λ₀ = 4L₀ ; We know f = v/λ, Hence, f₀ = v / λ₀ = v / 4L₀ ------Eqn (2)

Comparing Eqn(1) and Eqn(2), we find , f₀ of closed organ pipe = ½ times f₀ of open organ pipe which means

The fundamental frequency note of open organ pipe is twice the fundamental frequency note of the closed organ pipe.