Displacement-distance vs Displacement-time graphs for waves

[Suhayl Patel]

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?

 

[Simon Bridge]

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.