Phase difference in Stationary waves

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SUMMARY

The phase difference between two oscillating points located between adjacent nodes in stationary waves is zero. This can be demonstrated through calculations involving the expressions for progressive waves. By writing the expression for a wave traveling in the positive direction and another for the wave traveling in the opposite direction, and then adding them together, one finds that the resulting oscillation lacks an x term in the cosine function, indicating a phase difference of zero. The amplitude of the resulting wave will vary with position, confirming the stationary wave behavior.

PREREQUISITES
  • Understanding of stationary waves and nodes
  • Familiarity with wave equations and trigonometric functions
  • Basic knowledge of oscillatory motion
  • Ability to perform mathematical calculations involving wave superposition
NEXT STEPS
  • Study the derivation of wave equations for stationary waves
  • Learn about the concept of nodes and antinodes in wave mechanics
  • Explore the mathematical principles of wave superposition
  • Investigate the implications of phase differences in various wave phenomena
USEFUL FOR

Students of physics, educators teaching wave mechanics, and anyone interested in understanding the behavior of stationary waves and their properties.

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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