P1: Motion of a Traveling Pulse

(P1a) Velocity of the Pulse

Measure the pulse velocity, by measuring the position of the pulse at two different times and the time interval. Make sure the pulse does not get close to the edges during your measurement! You can run for a specified time using the ``Time to Run'' entry box. Be sure to type Enter after changing an entry box: if the number is red, the program hasn't read it in yet.

Write the formula for the pulse velocity as a function of the parameters of the simulation in your lab write up. Find the values for the important parameters using the Configure menu: Mu1 is the mass per unit length in kg/m: calculate the expected pulse velocity and write that in your lab write up. In your writeup, check to see how well your measured velocity agrees with the calculated one: it should work to two or more decimal places.

(P1b) Width of the Pulse

Measure the spatial pulse width (full width half maximum, as described in the intro to the simulation). Measure the FWHM duration in time, using the lower graph: write these in your lab write-up.

What should the ratio of the two kinds of pulse widths be? Write the formula for the ratio, evaluate it, and write it in your lab write up. Compare your prediction with the measured ratio: they should again agree to a couple of decimal places. Does the FWHM in time agree with that given by the Configure menu?

(P1c) Shape of the Pulse

Compute how long the pulse should take to make one complete round-trip starting from somewhere in the middle of the string (to the right end, back to the left, and forward again to the initial position). Include the formula in your write-up. Start with the pulse somewhere in the middle, and type the round-trip time in "Time to Run". Before you run the round trip, use the ``Copy Graph'' button at the middle right to save the original shape. Run the simulation, checking to see if indeed you calculated the round-trip time correctly. Use the ``steal data'' button (upper left hand button on the graph copy) to capture the new packet shape on the same graph. Does the shape stay roughly fixed?

(P1d) Weird Packets

The wave equation is supposed to work for any shape packet - not just nice round humps. Try selecting "Packet" from the Forcing menu on the upper left. Does this wave form also maintain its shape as it moves? As above, "Copy Graph", run for a round trip, and "Steal Data", making sure to fil in the box for "Your Name" first. Save the PostScript and print the figure for your writeup, unless instructed otherwise by your TA.

Links Back

Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).