If the fundamental frequency of a pipe closed at one end is 512 Hz. The fundamental frequency of a pipe of the same dimensions but open at both ends will be:

The fundamental modes of vibration of a pipe closed at one end and open at both ends (of same length) are shown in figure.

The wavelength in figure (2) is half of that in figure (1). Hence the fundamental frequency in figure (2) is double that in figure (1).

$\therefore {\mathrm{f}}_{\mathrm{open}} = 2\times 512 = 1024 \mathrm{Hz}$