We have seen that the source of electromagnetic waves is oscillating charges. All electromagnetic waves travel at the speed of light in vacuum. The quantity that distinguishes one electromagnetic wave from another is its frequency or wavelength. The faster the oscillation of the charges, the higher the frequency of the waves. Visible light corresponds to oscillations at 5´ 10¹⁴ Hz, radio waves are in the MHz range,etc. The different types of electromagnetic waves that are possible are referred to collectively as the electromagnetic spectrum.

There is a basic vocabulary that we have to acquire to discuss electromagnetic waves. First of all, electromagnetic waves are transverse waves; the electric field oscillates in a direction perpendicular to the direction of propagation. The simplest solution of the wave equation is an infinite, plane monochromatic wave characterized by a single frequency f and a single wavelength l. The wavelength l is the peak to peak distance of a snapshot of the field pattern at a given instant of time – its units are meters. The period T of the wave (units are seconds) (milli= 10^-3 ; micro=10^-6 , nano = 10^-9, pico =10^-12 ; femto=10^-15 ) is the time it takes for a complete oscillation of the wave at a fixed position. The frequency f=1/T is the number of oscillations per second (units are Hz) (kilo=10³; mega=10⁶, giga=10⁹, tera=10¹² , peta=10¹⁵ ). The speed of propagation of an electromagnetic wave in vacuum is the speed of light c. The basic relationship between speed, frequency and wavelength is c=fl.

There are other parameters used to describe waves. The angular frequency w=2pf=2p/T has units of radians/s, or simply s^-1 (see below). The propagation constant k is defined as k=2p/l. It then follows that w=ck. When you think of k, think of frequency since it is proportional to frequency.

The difference between Hz and radians/s is often confusing. One cycle is equal to one Hz which is equal to 2p radians. Therefore, a frequency of 1 Hz corresponds to an angular frequency of 2p radians/s. The term angular frequency is used since the up and down motion of the wave can be thought of as the projection on the x-axis of a particle going around in a circle with constant speed. It is useful to remember that a whole wave corresponds to one period T, one wavelength l, one cycle, or 2p radians. Thus half a wave is T/2, l/2, or p radians.

Superposition of waves. The infinite, plane monochromatic wave is the "building block" solution of the wave equation. All other waves can be built up from monochromatic waves having different frequencies and different amplitudes. The addition of waves is known as the superposition of waves. For waves having the same frequency, waves will add constructively if they are in phase – that is the relative phase of the wave is 2p, 4p, 6p, etc (adding peak to peak). They add destructively if the relative phase is p, 3p, 5p, etc (adding peak to trough). You can vary the relative phase and add waves by going here. Remember, saying the waves are in phase means they differ spatially by an integral number of wavelengths. Waves that are out of phase differ by a half integral number of wavelengths.

You can now understand the two-slit experiment. At the central point of the screen the light from each slit traveled an equal distance so the waves are in phase and there is a bright spot on the screen. As you move up the screen, the distance from each slit to the screen changes. When the path difference between light from the two slits is equal to half a wavelength, there is destructive interference and a dark spot on the screen. The pattern continues as you move along the screen. When the path difference is an integral number of wavelengths there is constructive interference. When the path difference is a half integral number of wavelengths there is destructive interference. The pattern is a series of bright and dark spots as seen in class.

Another interesting superposition pattern is a standing wave field. When you generate waves on a string that is clamped at both ends or electromagnetic waves between two mirrors, the wave pattern corresponds to waves moving to the left and right at the same time. The wave pattern in this case varies as sin(kz)cos(wt). There is a stationary envelope [sin(kz)] so that this pattern is called a standing-wave field. The field intensity goes to zero each half wavelength – such points are called nodes of the field. The distance between nodes in a standing wave field pattern is half a wavelength. We will use this result in the analysis of a black body.

Diffraction of waves. Another interesting wave phenomenon related to interference and Maxwell’s equations goes under the general heading of diffraction. If you try to restrict a wave to a distance less than or on the order of its wavelength, the wave will spread out or diffract. Imagine you are in a dark room with a pinhole in one wall that can let in light. If you look towards the pinhole you will see light that has been diffracted to your eye. Light no longer travels on straight line paths (with simple shadows) whenever you try to restrict it to distances less than a wavelength. When we get to quantum mechanics, we will see that this statement translates into the famous Heisenberg Uncertainty Principle.

Radiation pulses. Monochromatic waves are infinite in extent. To get a pulse of radiation having a width in time of Dt, it is necessary to superimpose monochromatic waves having a range of frequencies Df=1/Dt. Thus, the shorter the pulse you want, the larger the range of frequencies that is needed. If Df<<f₀ , where f₀ is the average frequency of the wave, the wave is said to be quadimonochromatic.