What properties of light are determined by wavelength?
The properties of light we can determine from the wavelength are the frequency and Energy - however, observing the source of the wavelength does lead to a host of other information.
The wave equation is
so knowing the wavelength we can determine the frequency and the Energy of the photon.
However, if the source of the light is known a whole set of information can be garnered from it.
e.g. the temperature and possible composition of the source - using the spectral line corresponding to the particular wavelength we are observing.
velocity of the source - using either Doppler law (or Hubble law in case of stars).
Distance from the source - by the inverse square law - a technique used in astronomy where similar stars in near and distant galaxies allow us to find the distance to those distant galaxies.
What material is present between the source and the detector (Absorption spectroscopy).
just to state a few.