There are two major kinds of waves: transverse waves and longitudinal waves. The
medium transmitting transverse waves oscillates in a direction perpendicular to the
direction the wave is traveling. A good example is waves on water: the water oscillates up
and down while transmitting a wave horizontally. Other common examples include a
wave on a string and electromagnetic waves. By contrast, the medium transmitting
longitudinal waves oscillates in a direction parallel to the direction the wave is traveling.
The most commonly discussed form of longitudinal waves is sound.
Transverse Waves: Waves on a String
Imagine—or better yet, go grab some twine and set up—a length of string stretched
between two posts so that it is taut. Each point on the string is just like a mass on a
spring: its equilibrium position lies on the straight line between the two posts, and if it is
plucked away from its resting position, the string will exert a force to restore its
equilibrium position, causing periodic oscillations. A string is more complicated than a
simple mass on a spring, however, since the oscillation of each point influences nearby
points along the string. Plucking a string at one end causes periodic vibrations that
eventually travel down the whole length of the string. Now imagine detaching one end of
the string from the pole and connecting it to a mass on a spring, which oscillates up and
down, as in the figure below. The oscillation at one end of the string creates waves that
propagate, or travel, down the length of the string. These are called, appropriately,
traveling waves. Don’t let this name confuse you: the string itself only moves up and
down, returning to its starting point once per cycle. The wave travels, but the medium—
the string, in this case—only oscillates up and down.
The speed of a wave depends on the medium through which it is traveling. For a stretched
string, the wave speed depends on the force of tension, , exerted by the pole on the
string, and on the mass density of the string, :
The formula for the wave speed is: