Phase difference in Stationary waves

[elemis]

I have a question.

Why is it that the phase difference between two oscillating points which are both located in between two ADJACENT nodes is zero ?

Can someone prove this via a calculation ?

 

[sophiecentaur]

Write down the expression for a progressive wave in x and t then write down the expression for a wave going in the opposite direction (negate the x term). Add them together for a range of x values and you'll find what you're looking for - you'll get an oscillation with no x term inside the cosine but an amplitude that depends on x.
Try that out for yourself first. I have done it in the past but not recently (can't be arsed!).