Although sound waves in air are longitudinal, here we’ll show the wave as
transverse so that it’s easier to determine the wavelength. Since the distance
between an antinode and an adjacent node is always of the wavelength, the length
of the tube, L, in the figure above is the wavelength. This is the longest standing
wavelength that can fit in the tube, so it corresponds to the lowest standing wave
frequency, the fundamental
The next higher-frequency standing wave that can be supported in this tube must
have two antinodes and two nodes.
In this case, the length of the tube is equal to 3( λ′), so