Phase difference and Standing waves vs Progressive waves

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SUMMARY

The discussion centers on the confusion surrounding phase differences in stationary waves versus progressive waves in the context of A-level physics. It is established that the phase difference between adjacent nodes is 0 radians, while between odd-numbered nodes, it is π radians. The participants clarify that stationary waves form when two progressive waves traveling in opposite directions have the same frequency, wavelength, and a constant phase difference. The conversation emphasizes the importance of accurately identifying nodes and antinodes to determine phase differences correctly.

PREREQUISITES
  • Understanding of wave mechanics, specifically stationary and progressive waves
  • Knowledge of phase difference concepts in wave theory
  • Familiarity with nodes and antinodes in wave patterns
  • Basic proficiency in A-level physics equations related to waves
NEXT STEPS
  • Study the principles of wave interference and how stationary waves are formed
  • Learn about the mathematical representation of phase differences in waves
  • Explore the conditions required for constructive and destructive interference in waves
  • Review examples of stationary waves in real-world applications, such as musical instruments
USEFUL FOR

Students studying A-level physics, educators teaching wave mechanics, and anyone seeking to clarify the differences between stationary and progressive waves.

Lamar Ngolo
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1495121023587-154927012.jpg
and

Homework Statement


Ok, so I am doing As physics at the moment and have been left confused by stationary waves.
I have read that between adjacent nodes/ even numbers the phase difference is always 0 and between numbers of does it is pi radians. So in the attatched image why is my textbook giving answers of 180, 225 and 0 degrees: this is what would be the case on a progressive wave, right?
Also, do stationary waves only form where 2 progressive waves in opposite directions have the same frequency, wavelength and constant phase difference, or only a few of the named conditions needed?

Thanks everyone

Homework Equations


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The Attempt at a Solution

 
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Lamar Ngolo said:
between adjacent nodes/ even numbers the phase difference is always 0 and between numbers of does it is pi radians.
That is rather garbled. Please clarify.

With regard to the question, I do not understand how you are supposed to know exactly where B is.
 
haruspex said:
That is rather garbled. Please clarify.

With regard to the question, I do not understand how you are supposed to know exactly where B is.
I was meant to put between odd numbers of nodes is the phase difference pi radians?
 
Lamar Ngolo said:
I was meant to put between odd numbers of nodes is the phase difference pi radians?
Ok.
In this question, O, A and C are antinodes, but the same method applies.
Counting from O, how many antinodes away is A? Is that an even or odd number?
How about from O to C?
 
haruspex said:
That is rather garbled. Please clarify.

With regard to the question, I do not understand how you are supposed to know exactly where B is.
haruspex said:
Ok.
In this question, O, A and C are antinodes, but the same method applies.
Counting from O, how many antinodes away is A? Is that an even or odd number?
How about from O to C?
Would it not just be Pi rad for A and B and 0 for C?
 
Lamar Ngolo said:
Would it not just be Pi rad for A and B and 0 for C?
π For A and 0 for C, but B is not at a node or antinode. As I wrote, from the information given, I don't know how you are supposed to know exactly where B is.
 

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