Gravity Related Standing Waves in Plants

Leaf and branch spacing are termed internodal spacings (1/2 wavelengths here) in the literature. There is apparently a unique set of available 1/2$\lambda $' s with the choice determined by growing conditions. The ratio of the usually larger vertical velocity to the horizontal wave velocity is apparently determined by the genotype and shapes the plant. The ratio for a particular plant can often be found by measuring several hundred vertical and horizontal spacings and taking reciprocals. Then find the horizontal reciprocal average A$_{h }$and do the same for the vertical to get A$_{v}$ Then equating frequencies v$_{v}$A$_{v}$=v$_{h}$A$_{h}$ (also equals similar terms for other 5$^{o}$ integral$^{ }$multiples) gives v$_{v}$/v$_{h}$=A$_{h}$/A$_{v}$. Standard deviations for A$_{v}$ and A$_{h}$ are in the range of 15-50{\%}. The ratios, however, are nearly exactly (usually within 1{\%}) ratios of small integers like 3/1 for Ponderosa pine.$_{ }$In species, where higher frequencies dominate, one can often measure cell lengths as half wavelengths and similarly arrive at the velocity ratio. Velocities are found by disturbing the standing waves and plotting the resultant electrical signal from spaced probes as a function of time. See chatlink.com/$\sim $oedphd