How Do Two Superposed Waves Result in Points of Zero Displacement?

[socoil23]

Homework Statement

given 2 waves y1=Ysin(kx-wt): y2=Ysin(kx+wt).
derive expression of resultant displacement and expression of x(for resultant) where displacement always zero

Homework Equations

y=y1+y2
sinA+sinB=2sin((A+B)/2)cos((A-B)/2)

The Attempt at a Solution

i solved first part:y= 2Y sin (kx) cos (-wt)
but i don't understand the 2nd part. does it mean y=0 when sin kx=0? mean x=0?

 

[kuruman]

Is x = 0 the only value of x at which sin(kx) = 0?

 

[socoil23]

I had figure it out.displacement is directly related to sin kx.displacement is Zero when kx equal to n*pai
where n is integer.displacement always zero when x = n*pai/k.