# Electromagnetic wave frequency and wavelength relationship

### Wavelength - Wikipedia

electromagnetic radiation with shorter wavelengths is more energetic. The relation- ship between energy and frequency is given by the equation, E = hν, where h. Because all light waves move through a vacuum at the same speed, the The equation that relates wavelength and frequency for electromagnetic waves is. see has a particular frequency - Here, the key relationship is shown with worked i.e. part of the electromagnetic spectrum, and so travel at the speed of light.

The figure shows waveforms of two different wavelengths - the lower wave has a shorter wavelength than the top wave. If both waves are traveling at the same speed, then in observing the bottom wave from a fixed point, we would see more peaks passing us per unit time than if we were watching the top wave.

Wavelength frequency and energy

Thus, the bottom wave would have a higher frequency than the top wave. In fact, an important relationship that holds for all waves is the following: We may also find it necessary to use decimal multipliers for unit conversion, as frequencies and wavelengths of EM radiation vary over many orders of magnitude.

As stated above, waves carry energy, but how much energy? The energy a wave carries is related to its amplitude, which is one-half the distance between the wave's crest highest point and trough lowest point. We can readily agree that a tsunami carries much more energy than a pond ripple.

The amount of energy delivered by travelling waves such as ocean waves, sound waves, or the waves of EM radiation is time-dependent, so we can alternatively relate wave amplitude to power, or energy per unit time.

## Light: Electromagnetic waves, the electromagnetic spectrum and photons

The power carried by a wave is proportional to the square of its amplitude and the square of its frequency.

A related quantity, intensity I is defined as the power transmitted by the wave per unit area normal to the direction of propagation. Waves such as light or sound from a point source are three-dimensional, as opposed to the one-dimensional waveform shown above. The intensity of a wave is also proportional to the square of the wave amplitude. Such repeating functions are termed periodic functions.

### How are frequency and wavelength related?

We can introduce a phase factor into the waveform by adding a term to the argument of the sine function. The argument is the expression inside the parentheses that gives the value that one would "take the sin of".

Another way of saying this is that the argument of a function [such as exp, log, sin, cos, The next section solves the equation as it is, and there is a calculator for frequency, wavelength and speed here.

Solving the Equation In this example we will consider the frequency of radio waves. Radio waves are just another form of "light", i. Let's say we have a radio with a dial that is only marked in MHz. This is a measurement of frequency and we note that 1 MHz is the same as 1 million hertz the M in MHz stands for " mega ", which means million. We are told of a radio broadcast we want to hear but we are only given the wavelength of the station and not the frequency.

The wavelength we are given is 3. We know the speed of light and we know the wavelength so it's now an easy matter to plug these numbers into the equation and find the frequency of the radio station: This gives us a frequency of 92 MHz, which is found in the FM range of most domestic radios. Visible Light The wavelengths of visible light are measured in nanometres, nm billionths of a metre but the equation works just the same. When we look at a light source the colours we see are dictated by the frequency of the light.

Separation occurs when the refractive index inside the prism varies with wavelength, so different wavelengths propagate at different speeds inside the prism, causing them to refract at different angles. The mathematical relationship that describes how the speed of light within a medium varies with wavelength is known as a dispersion relation.

### Speed, Frequency and Wavelength - How they are related, with examples

Nonuniform media[ edit ] Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore [11] Wavelength can be a useful concept even if the wave is not periodic in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying local wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth.

The figure at right shows an example. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response, the short wavelength is associated with a high loss and the wave dies out.