Traveling Waves

"The essence of science: ask an impertinent question, and you are on the way to a pertinent answer"
Jacob Bronowski

Imagine a sequence of particles undergoing identical Simple Harmonic Motion, such that each particle begins to move slightly after the one before it. The result is a traveling "Wave Motion". If all the particles are connected, for example, in a string, the motion is described as a continuous "Sine Wave".
The Sine Wave is the simplest of all possible waves. A periodic wave is one in which the shape of the wave is repeated "periodically" - at regular fixed intervals.

Wavelength () - Distance after which the wave begins to repeat (Units: metres).
Frequency (f) - Number of waves passing a fixed point in one second (Units: Hertz).
Wave period (T) - Time taken for one wave to pass a given point (Units: seconds).
Wave speed (v) - Distance travelled by the wave per second (Units: m/s).
Amplitude (A) - Maximum displacement of particle which comprise the wave from their equilibrium position (Units: metres).

TRANSVERSE : Motion of the constituent particles is at right angles to the wave direction, e.g. waves on a string, "stadium" wave, electromagnetic waves.

LONGITUDINAL : Motion of the constituent particles is back and forth in the direction of motion of the wave, e.g. sound waves, the " Slinky " spring.

The amplitude of the SHM of the particles which comprise a Sine Wave is the same as the amplitude of the wave.
The frequency of the SHM of the particles which comprise a Sine Wave is the same as the frequency of the wave.
Particles which comprise the wave typically do not move at the speed of the wave, e.g. molecules of air do not move at the speed of sound in air.

A wave "travels" from A to B. The particles that comprise the wave do not move from A to B, they oscillate about their fixed (equilibrium) points.
A wave transmits energy from one point to another.
Water waves appear to be transverse - boats bob up and down due to water waves. However, a detailed study shows that the molecules of water actually perform a circular motion, which can be considered as a combination of transverse and longitudinal wave motion.
Fourier's theorem states that any periodic wave can be decomposed into a sum of sine waves with differing frequencies and amplitudes. This means that an analysis of the properties of sine waves can be applied to any periodic wave.

"In a packed program tonight we will be talking to an out-of-work contortionist who says he can no longer make ends meet."

Ronnie Barker

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu