How Do You Graph Wave Displacement Over Time for Point P?

[simon123]

Hey everyone, I've just stumbled across this forum on Google while trying to find something to help me understand a question.

I've just started studying physics at AS level at sixth form, and I've been given this piece of homework, with the teacher not explaining it too well, so, I'm stuck.

There is a diagram on the sheet (link below) and two questions, I've tried the first one by using help from diagrams and things I've found on the net, but it turned out completely wrong. And I have absolutely no idea at all for question 2.

I don't expect somebody to do it all for me, but if anyone can explain what I need to do, or give me any pointers it would be greatly appreciated, as I really want to understand this!

http://img217.imageshack.us/my.php?image=homeworkwv1.jpg"

1 - Draw three new sets of axes, one below the other, and draw the waveform observed after one second, two seconds and three seconds.
2 - You have drawn wave displacement against position graphs. On a separate sheet of graph paper draw a displacement against time graph for point P over the three second period.

Thanks to everyone in advance

 

[loonychune]

The graph you link to shows the displacement of the wave at zero seconds... at point P the displacement of the wave is zero... so at t = 0 the displacement = 0...

At t = 1 second both those 2 waves shown in the image have moved towards P... in fact they've both moved two places... look what you get at P.. the left wave has its maximum displacement at P and the right wave has its maximum displacement at P... so you add those two displacements together... so you get a displacement at t = 1 second that is twice as high as the top of the two waves shown...

At t = 2 the waves again move two places (speed = 2m/s) left and right accordingly... look again at the displacements at P and add them... i.e. 'superposition them'...

 

[simon123]

Thanks for your quick reply, I actually understand question 2 now, I had absolutely no idea before!

However, you said that both waves are at their highest displacement at P when t = 1. I can see why the wave on the left is, but why the wave on the right? The wave on the right has a vertical line, so why have you chosen the point at the top and not the point on the x axis?

It's that which has got me so confused, if they were both like the wave on the left I'd be able to do it *sigh* if only...

Thanks

 

[loonychune]

Ah yes it got me thinking a little bit did that.

I suppose the way i see it is this:
There is no disturbance in space. Then at some point there in space there comes, INSTANTANEOUSLY (since the wave is traveling it's fair to say 'instantaneous') a signal and hence the wave has amplitude (the vertical line means that the rate of change of amplitude is infinite so going up the vertical line to the horizontal is done in zero time). It remains at that amplitude along the horizontal line and then instaneously falls to some lower amplitude.. and so on...

The square wave is really just an idealised pulse (it can't in reality go instaneously to some amplitude, it will take some time)... if you go to this link here you can see how you use lots of harmonic waves to add up to the square wave...

http://en.wikipedia.org/wiki/Image:Synthesis_square.gif

Hope this makes things reasonably clearer...

(I ought really spend some time studying waves again myself i realize!)