Ph 385

Fall 2006

Fourier 2:  The triangle standing Wave

( PH 385 home page |Fourier series coefficients | logon and setup )

I.  Logging on and running IDL.

Start by logging onto the P&A computer system, starting the desktop, opening a terminal (or xterm) window, and changing to a subdirectory for this problem.  (See previous problems Wave-1 and Wave-2 for details about logging on and starting IDL.)  Just after opening the terminal window, enter

cd ph385

mkdir fourier2

cd fourier2

pwd

You should get back (or at least I did)

            /Users/faculty/bland/ph385/fourier2

Open a couple morej xterm windows, and start IDL in one of them.

II.  Making the wave move.

Here you should start with the program file you made for the problem Fourier-1.  Copy it over like this:

cp ../fourier1/fourier1.pro ./fourier2.pro

(Look out for periods - they have to be there.)  Run this program, to make sure it still works.

            IDL> .rnew fourier2

            IDL> fourier1

Now open the file fourier2.pro with pico and make some changes.

   * Change the internal name to fourier2, to match the file's name.

Change the file to look like this:

PRO fourier2

black=0

white='ffffff'x

   !p.background=white

   !p.color=black

read,'Number of terms: ',nterms

   L=2.

   x = findgen(401)/200.; vector of 401 floating-point numbers, from

                        ; 0.0 to 2.0 .

   y=fltarr(401); y starts a a vector of zeros.

   v=2.0; wave speed, in m/s

dt=0.05; time step

   FOR itime=0,100 DO BEGIN

      t=itime*dt

      y=fltarr(401); reset to zero each time.

      FOR n=1,nterms,2 DO BEGIN

an = 8./(!pi^2*n^2)*(-1)^((n-1)/2); nth coefficient

kn=n*!pi/L

omegan=kn*v

         y = y + an*sin(kn*x)*cos(omegan*t); add on nth term

      END

plot,x,y,title='Triangle wave, nterms = '+string(nterms)

   END

END

Can you see the reasons for the changes?  We now are giving the argument

to the n-th sine wave, where k_n and w_n are made up using a wavelength of 4 meters (twice L) and a wave speed of 2 m/s.  This should make the wave vibrate with a period of 2 seconds.  The times are generated by a second loop, over the variable itime.

Run this program.  It works pretty well, but runs too fast.  Here is the way to slow it down.  Put

            str1=""; input buffer

near the front of the program, and the command

read,str1

after the plot statement.  Then the program will wait while you look at the n-th iteration.

Next you may want to plot successive time steps on the same plot.  To do this, add a first plot statement just after the time step, like this:

dt=0.05; time step

plot,x,y,xrange=[0,2],yrange=[-1,1],title='nterms: '+string(nterms)

This draws the axes.  Then change the plot statement near the end to the simpler form

oplot,x,y

This should be enough to let you see what happens to the triangle wave when you let go!

You might fool around with the time, like making it not quite so even a number so that you can see successive plots.  And you could comment out the read statement,

            ; read,str1

and let the program go as fast as it can!

   Record and document what you have done as usual.

   Explain what you learned about wave propagation on a string from these calculations.