I'm unclear about the entire idea of why if a string fixed at 2 ends is plucked at a point, say L/3 from the left, the node at the pluck point and any node that is a multiple integer of 3 would be unexcited. Trying to see it mathematically, and I've only been able to arrive at is this. mL=nλ At (1)(L/3), we have L/3 = 3λ At (2)(L/3), we have 2L/3 = 6λ and so on. So, if the string is plucked at L/3, the only wave length that can be arised on the string are n-multiplers of λ. 3λ, 6λ, 9λ....etc.