Waves

amplitude of node = 0 . then k = ∞ ?

No. The amplitude isn't exactly zero.

I too did it using the fact how the Amplitudes and the Energy for a wave are related . We have expression for the Amplitude of the reflected wave and from there we can get it.

Did you do the same way or else?

let wave be x=Asin(wt)
reflected wave=Bsin(wt+Ï€) [B due to loss of energy,Ï€ phase change due to reflection]
therefore eqn. of stationary wave=Asinwt-Bsinwt=(A-B)sin(wt)

Therefore amplitude at node should be 0.

Aditya, Post you solution please.