Think of waves as a means of transmitting energy over a distance. One object can
transmit energy to another object without either object, or anything in between them,
being permanently displaced. For instance, if a friend shouts to you across a room, the
sound of your friend’s voice is carried as a wave of agitated air particles. However, no air
particle has to travel the distance between your friend and your ear for you to hear the
shout. The air is a medium, and it serves to propagate sound energy without itself having
to move. Waves are so widespread and important because they transmit energy through
matter without permanently displacing the matter through which they move.
Crests, Troughs, and Wavelength
Waves travel in crests and troughs, although, for reasons we will discuss shortly, we
call them compressions and rarefactions when dealing with longitudinal waves.
The terms crest and trough are used in physics just as you would use them to refer to
waves on the sea: the crest of a wave is where the wave is at its maximum positive
displacement from the equilibrium position, and the trough is where it is at its maximum
negative displacement. Therefore, the displacement at the crest is the wave’s amplitude,
while the displacement at the trough is the negative amplitude. There is one crest and one
trough in every cycle of a wave. The wavelength, , of a traveling wave is the distance
between two successive crests or two successive troughs.
Wave Speed
The period of oscillation, T, is simply the time between the arrival of successive wave
crests or wave troughs at a given point. In one period, then, the crests or troughs travel
exactly one wavelength. Therefore, if we are given the period and wavelength, or the
frequency and wavelength, of a particular wave, we can calculate the wave speed, v: