Close a pipe at one end and the rules change. The closed end pins the air still — a node — while the open mouth swings free — an antinode. The simplest wave that manages both is a QUARTER of a wavelength, so $\lambda = 4L$ and $f_1 = \dfrac{v}{4L}$ — read aloud: f-one equals v over four-L. Same speed, same length: a closed pipe sounds an octave below the both-ends string. The 4 is the whole difference.

Stranger still: a closed pipe plays odd harmonics only — $f_1, 3f_1, 5f_1$. The even multiples would need the closed end to move, and it won't. This is the SPH3U resonance-tube lab: a tuning fork over a tube of water, and the column sings when its length hits a quarter wavelength.