Waves & Pulses

A wave is a disturbance in a medium that transfers energy.  These "disturbances" can be analyzed as Simple Harmonic Motion.

The smallest part of a wave, acting on one single particle of a medium is called a pulse.  The sum of all pulses make up the wave pattern.

Here is an example of a transverse pulse.  Here you will see the particle being displaced perpendicularly to the direction of travel of the pulse.


There are three main types of waves:

  1. Longitudinal
  2. Transverse
  3. Surface

In longitudinal waves the particles of the medium move perpendicularly to the motion of the wave.

Example: sound is a longitudinal wave

In transverse waves the particles of the medium move parallel to the motion of the wave.

Example: a guitar string vibrating when struck

In surface waves the particles of the medium move in circular patterns relative to the motion of the wave

Example: water waves created by a rock dropped in a pond

 web4 External resources: http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html

Period, Frequency, and Amplitude

wave properties

Properties of a Wave

Refer to the above diagram

Amplitude: The maximum displacement (measured in linear units --meters, centimeters, nanometers, etc.) of the particles of a medium due to the action of a wave or pulse or other harmonic disturbance.

Period:  The time it takes a wave to complete one entire cycle.   The symbol for period is “T”.  The unit for period is the second (s).

Frequency:  The number of repeated actions per unit time.  When we talk about the frequency of a wave we define frequency as the number of cycles per unit time.   The symbol of frequency is “f”.  The unit of frequency is the cycle/second or the Hertz [Hz].

The relationship between frequency and period is that Period is the reciprocal (or the inverse) of frequency and vice versa. 

In mathematical symbols:

frequency period eqn

The Universal Wave Equation:

The universal wave equation tells us that the speed of a wave depends on its frequency and its wavelength.  This equation can be derived from simple equations of motion.


  1. Recall that  V = d/t     (total distance/total time). 
  2. Consider one full cycle of a wave or one wavelength.  The total time elapsed in this cycle is the period of the wave (T) and 
  3. Recall that   T = 1/f
  4. The total distance traveled in one cycle is in fact the wavelength l.

Now, substituting these symbols in the equation  v = d/t  we obtain

Univ wave eqn derived

The equation  

Univ wave eqn

is known as the Universal Wave Equation because it applies "universally" to all types of waves traveling in any medium.