I'm trying to find how the wave equation was derived in 3 dimensions.
Surprisingly, there isn't much information available on this apart from wikipedia of all places
https://en.wikipedia.org/wiki/Wave_equation#Scalar_wave_equation_in_three_space_dimensions
It mentions that Euler discovered it and a derivation is based on a solution to a spherical wave.
What I don't understand is where this information is from. If anyone knows a good source then please let me know.
The other 2 small questions I have concern the third equation underneath the relevant section which has the $$ f_{lm}(r) $$ expression.
What does l, m, r and the above expression represent in this case?
Many thanks in advance.