Wave Characteristics

Waves can be described in terms of wavelength, $\lambda$, and frequency, f. They are oscillations in time and also as a function of position for a given time. One can combine these two oscillations into the equation of motion for a simple wave:

y(x,t) = A sin(2$\pi$ft + 2$\pi$x/$\lambda$+ $\delta$)

Here, again, $\delta$ is the phase shift. Sometimes you can also find this equation written as

y(x,t) = A sin($\omega$t + kx+ $\delta$)

where $\omega$= 2$\pi$f is the angular frequency, and k = 2$\pi$/$\lambda$ is the wave number. One can show that the wave velocity is then given by

v = $\lambda\cdot$f

which is always valid for all types of waves. This short equation might be the one that is most important of all equations in this chapter.

In general the intensity of a wave is proportional to the square of both the amplitude, A, and the frequency, f, of the wave,

I = constant $\cdot$ A² · f²

There are two basic kinds of waves, transverse waves and longitudinal waves:

A transverse wave is one in which the motion of the particles is perpendicular to the direction the wave is traveling. Example are a vibrating string or water waves. In the second semester of this course we will also see that electromagnetic waves, such as light waves, are transverse. Electromagnetic waves do not need a carrier medium at all.
A longitudinal wave is one in which the motion of the particles is parallel to the direction the wave is traveling. The most common example is sound. Longitudinal waves can travel in solids, liquids, and gases. To see the difference between a transverse and a longitudinal wave in a more or less realistic simulation click the button below.