Wave Motion
The animation shows progressive propagation of two sinusoidal waves driven by fast (animation at top) and slow (animation in the middle) oscillators. The frequency difference is by a factor 2. Note that the wavelength is elongated by a factor of 2 if the driver frequency is halved. Both waves propagate at the same speed. Sinusoidal waves can be described by
where A is the amplitude,
is the wavenumber, and
is the oscillation angular frequency.

Waves do not have to be sinusoidal in contrast to oscillations. The animation at the bottom shows propagation of an exponential pulse wave. An arbitrary (well behaving) function in the form

satisfies the wave differential equation
where cw (m/sec) is the wave propagation velocity.

> with(plots):
animate(sin(.25*t-x)*Heaviside(.25*t-x),x=0..30,t=-1..120,frames=50,color=red,numpoints=100,thickness=2);
animate(sin(.5*(.25*t-x))*Heaviside(.5*(.25*t-x)),x=0..30,t=-1..120,frames=50,color=red,numpoints=100,thickness=2);

[Maple Plot]

[Maple Plot]

> animate(exp(-(.25*t-x)^2),x=0..30,t=-1..120,frames=50,color=red,numpoints=100,thickness=2);

[Maple Plot]

>