Pulse Traveling on an Elastic String

time

0.46

This Demonstration shows the behavior of a pulse (a local deformation) in an elastic string. The pulse travels at a constant speed in the positive

x

direction, so that at any instant only a limited region of the string is disturbed. Do not confuse the speed of the pulse with the velocity of a point in the propagation medium, shown by the red point on the elastic string.

The function describing the pulse is

y(x,t)=f(x-vt)

, where

v

is the speed of the pulse in the direction

x>0

. The position (black line) of a specific point in the propagation medium (red point) is obtained by fixing the position

x

and changing the time

t

in the function

f(x-vt)

. The velocity (blue line) and acceleration (brown line) of this point are given by the first and second derivatives of the function over time, respectively.

In this Demonstration we see the pulse traveling along the positive

x

direction in the bottom panel. The position

ψ

, velocity

v

, and acceleration

a

of the red point over the elastic string are show in the upper panel; the acceleration is zero at points where the velocity is a maximum.