Einstein's Second postulate of Special Relativity

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.

This means that we will always see light moving at

3.00 x 108 ms-1.

In equations we use a lower case c for the speed of light.

( c = constant)

Because the speed of light is a constant, when frequency is increased wavelength decreases.  This is important to understand because Energy and Frequency are directly related (Think about vibrating your finger up and down it requires more energy to vibrate them faster than slower)

Light, Energy and Momentum

(yes light has momentum)

In the late 19th century involved a contradiction between the wave theory of light and measurements of the electromagnetic spectrum emitted by thermal radiators, or so-called black bodies. Physicists struggled with this problem, which later became known as the ultraviolet catastrophe, unsuccessfully for many years. In 1900, Max Planck developed a new theory of black-body radiation that explained the observed spectrum. Planck's theory was based on the idea that black bodies emit light (and other electromagnetic radiation) only as discrete bundles or packets of energy. These packets were called quanta, and the particle of light was given the name photon, to correspond with other particles being described around this time, such as the electron and proton. A photon has an energy, E, proportional to its frequency, f, by

$E = hf = \frac{hc}{\lambda} \,\!$

where h is Planck's constant, λ is the wavelength and c is the speed of light. Likewise, the momentum p of a photon is also proportional to its frequency and inversely proportional to its wavelength:

$p = { E \over c } = { hf \over c } = { h \over \lambda }.$

As it originally stood, this theory did not explain the simultaneous wave- and particle-like natures of light, though Planck would later work on theories that did. In 1918, Planck received the Nobel Prize in Physics for his part in the founding of quantum theory.

(definition from Wikipedia)

Why do we choice the wavelengths we do?

Why do we use wavelengths of kilometers for Radio and  Television signals, and microwaves for cellphones.  Why do bats use ultra high frequency sounds for finding its prey (I know its sound and not light but its the same premises).

Long wavelengths

When radio and later televisions started appearing in living rooms across the country, we needed a method of delivering "light" (raido waves) to the masses. Construction and maintence of radio towers and the cost of electrical energy that just dumped into the air, were major concerns.  To reduce the numbers of towers and the amount of energy needed we use the longer wavelengths

How do longer wavelengths  reduce the number of towers.

Because the lengths of the radiowaves are in kilometers and up to hundreds of kilometers, it can pass by obsacal  that are the size of half the wavelength.  The path of the wave simply go around the obstical.  So that means radio waves can go around mountains and forests and one tower can service a large area.

Short Wavelengths

We use microwaves for point to point (cellphone) communication  because longer waves are less like to intersect objects so it's less likely to intersect your cellphone.   So in order to get a strong signal we need we need "obstructions" of the signal, so a shorter wavelength.  The down side is, its eaiser to block a  signal (you always loss signal when you are in the back of a building), and it costs more energy to produce a signal.