Chapter 9
Waves
Having examined simple harmonic motion, we are now in a position to examine waves. Awaveis a dis-
turbance in a material medium that propagates itself through the medium.^1 In a harmonic wave, each parti-
cle in the medium undergoes simple harmonic motion, but adjacent particles are slightly out of phase with
each other, which results in the wave disturbance propagating through the medium while the particles of the
medium itself simply oscillate in place.
9.1 Types of Waves
There are two major types of waves:
- Transverse waves.Particles of the medium moveperpendicularto the direction of wave motion. Trans-
verse waves can travel in solids only; they cannot propagate in fluids. - Longitudinal waves.Particles of the medium moveparallelto the direction of wave motion. Longitu-
dinal waves can propagate in both solids and fluids.
You can create a transverse wave in a long string under tension by giving it a quick flip at one end.
The disturbance will propagate down the string, although any point on the string will move up and down,
perpendicular to the string.
You can create a longitudinal wave by stretching a Slinky toy (or other spring) and giving it a quick in-
and-out “pulse” at one end. You’ll see the coils of the Slinky be alternately close together and spread apart
as the disturbance propagates down the length of the spring. A region where the coils are close together is
called acompression, and a region where the coils are far apart is called ararefaction.
Some waves are neither transverse nor longitudinal. For example, if you examine water waves in the
ocean, you will see that particles on the surface move in cycloid-looking paths that have both components
both parallel and perpendicular to the wave velocity—so water waves are a combination of transverse and
longitudinal waves.
You can create a singlewave pulseby giving the medium a single displacement at one end; the resulting
pulse will then propagate through the medium. You can also follow one pulse by another continuously,
resulting in awave train. For example, you can displace one end of the medium with simple harmonic
motion, and you will see a continuous wave train propagating through the medium. This will result in a
harmonic wave, which can be represented mathematically as
y.x;t/DAcos.
x!tCı/: (9.1)(^1) There are some notable exceptions: electromagnetic waves, quantum-mechanical waves, and gravitational waves do not require a
physical medium in which to propagate.