Adding Simple Harmonic Waves II is a Java applet which demonstrates the superposition of
two traveling simple harmonic waves. The applet can be used to illustrate phenomena in both
dispersive and non-dispersive media. For non-dispersive media, the user must enforce
| w1/k1| = |w2/k2| when specifying input values.
You can change the amplitudes: A, wave numbers: k = 2*pi/lambda,
and angular frequencies: w = 2*pi*f of two waves which will be combined
to form a third wave. Recall that v = lambda*f, so after you adjust an
individual wave it will have a speed of v = w/k. Positive velocities correspond
to motion to the right. To reverse the direction of motion, enter
a negative frequency or wave number.
A short theoretical background on this phenomena is availible in
dvi,
postscript or
pdf formats.
Things to do
Standing Waves
Create Standing waves by creating waves of the same wavelength and frequency traveling
in the opposite direction. Try for example:
w1 = 0.2, w2 = -0.2,
k1 = 0.05, k2 = 0.05,
Investigate Group and Phase Velocities
The "phase velocity", the velocity of the carrier wave is denoted by vph. vph = (w1 + w2)/(k1 + k2).
The "group velocity", the velocity of the the modulation, propagates at the vg.
vg = (w1 - w2)/(k1 - k2).
which, in general, may be greater than, equal to, or less than the phase velocity of the
carrier.
Recall that wave speed is related to the angular frequency and wave number by: v = w/k
A nondispersive media is one in which the velocity of a wave is independent of the wavelength
v(k) = const. For example the speed of light in vacuum is a constant
c = 3 x 108 m/s2
