Phase difference in Stationary waves

AI Thread Summary
The phase difference between two oscillating points between adjacent nodes in stationary waves is zero due to their synchronized oscillation. By calculating the expressions for a progressive wave and its opposite direction counterpart, one can demonstrate this phenomenon. When these two wave equations are combined, the resulting oscillation lacks an x term in the cosine function, indicating no phase difference. The amplitude of this combined wave varies with position, but the oscillation itself remains in phase. This illustrates the fundamental behavior of stationary waves in a defined medium.
elemis
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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 ?
 
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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!).
 

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