Question

Two sinusoidal waves travel in the same direction and have the same frequency. Their amplitudes are Y1 and Y2. The smallest possible amplitude of the resultant wave is:
a) Y1 + Y2 and occurs if they are 180 degrees out of phase
b)[Y1 - Y2] and occurs if the are 180 degrees out of phase
c) Y1 + Y2 and occurs if they are in phase
d) [y1-Y2] and occurs if they are in phase
e) [Y1-Y2] and occurs if they are 90 out of phase

My thoughts:
All the explainations of resultants in my book for waves show Y1+Y2=Resultant for the theory of superposition. So I think then to get the smallest wave it would be A. Y1 + Y2 if they are 180 degrees out of phase.

The displacement of a string is given by
y(x,t)=Ysin(Kx + wt)
speed of the wave is
a)2pik/w
b)w/K
c)wk
d)2pi/k
e)k/2pi

Work:
v=lamba*f
k=2pi/lambda
w=2pi/T
v=2pi/lambda * 2pi/(1/f)
v=w/k
so I choose b


Help is appreciated :)