General Properties of Waves

We first introduce some terminology associated with waves. Let us imagine that we drop a rock in the middle of a still pond and watch the waves emanating out from the center. From above the wave crests might appear as in Fig. 22.2.

  

Figure 22.2: Wave crests as seen from above

We assume the wave pattern is regular, and consider the following characteristics of these waves.

Definitions

• The wavelength ( $\lambda$ ) is the distance between neighbouring crests or troughs.
• The speed ( v ) is the rate at which the crests (or troughs) move forward.
• The Period ( T ) is the time that elapses between passing crests (or troughs). The period can be expressed in terms of the speed and wavelength:

  T = $${\lambda\over v}$$.

• The frequency ( f ) is the number of crests (or troughs) that pass by per unit time. It is equal to the inverse of the period:

  f = $${1\over T}$$.

  Using the expression for T above we get the useful expression:

  v = f$$\lambda$$.

• A ray is a line drawn from one wave crest to another which intersects each crest at right angles, as in Fig. 22.3. For light waves, the rays always point in the direction of the motion. Rays therefore provide a useful representation for describing the motion of light waves.
  
    

  Figure 22.3: Relationship of rays to wave crests

  
  
  

Note: Wave crests coming from a point source (eg. if you drop a rock in the middle of a still pond) give rise to circular waves as shown in Fig. (22.2). If one has very many point sources close together and in a straight line, they give rise to plane waves, whose crests all lie in a straight line. (See Fig. (22.4))

  

Figure 22.4: Plane waves formed by many point sources