**This animation** is based on a section of the (*forthcoming*) book,
* SPECIAL RELATIVITY ILLUSTRATED,* by John de Pillis.

**IMAGINE a PROPAGATED WAVE** to be a sequence of (*circular or spherical*) ripples,
each of which is created at the moment
a dancer's toe touches a point in the plane.

**AS THE DANCER MOVES on a PLANE, **
each of his landings sets of a single ripple with fixed speed *v*.
Once the ripple center is created by the dancer, it remains fixed in space
while its generated ripple continues to widen with a radius expanding at
fixed speed *v*.

**REGARDLESS of the DANCER'S SPEED,** therefore,
the speed of each ripple that is generated by the toe of the dancer
does
*NOT DEPEND ON THE SPEED OF THE DANCER'S TOE.*

**EXAMPLE:** Sound waves heard from a moving train have constant speed,
regardless of the train's speed. However, the waves will "bunch up"
ahead of the train, causing a higher tone, and they will "lag" behind the train,
causing a lower tone. This is the **DOPPLER EFFECT** for propagated waves.