Displacement-distance vs Displacement-time graphs for waves

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SUMMARY

The discussion clarifies the distinction between displacement-distance and displacement-time graphs for transverse waves, specifically using the equation y=A sin(kx). The displacement-distance graph represents the wave's shape at a specific moment, appearing as a sine wave. In contrast, the displacement-time graph illustrates how displacement varies over time for a fixed position, resulting in a horizontal line. This fundamental understanding is crucial for analyzing wave behavior in physics.

PREREQUISITES
  • Understanding of transverse waves and their properties
  • Familiarity with wave equations, specifically y=A sin(kx)
  • Knowledge of graphing techniques for mathematical functions
  • Basic concepts of wave motion and particle displacement
NEXT STEPS
  • Study the characteristics of transverse waves in detail
  • Learn how to derive and interpret wave equations
  • Explore graphical representations of wave phenomena
  • Investigate the applications of displacement-time and displacement-distance graphs in real-world scenarios
USEFUL FOR

Students and educators in physics, particularly those focusing on wave mechanics, as well as anyone seeking to deepen their understanding of wave behavior through graphical analysis.

Suhayl Patel
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Hi guys,
I'm finding it hard to conceptualise the difference between a displacement-distance and displacement-time graphs for transverse waves. Could somebody explain the difference please?
 
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With a wave like ##y=A\sin kx## you can see that the displacement (y) varies with distance (x) from some origin, but it does not vary with time. The the displacement-distance graph would be a sine wave, while the displacement-time graph (for each value of x) is a horizontal line.

More generally: you draw a displacement time graph for a particular value of distance x to see how the displacement of the particle associated with that point varies with time; or you can draw a displacement-distance graph for a particular instant of time to see a snapshot of the whole wave at that time.
 

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