When an electrically charged object moves it changes the surrounding electric field.  The change will propagate outwards at the speed of light.  The next picture shows an example made using an oscilloscope.

A paper-clip was put into the input socket of an oscilloscope.  A piezo-electric gas lighter was squeezed slightly, to make a high voltage, and moved past the clip.  The top trace shows the changes in the electric field.  The trace oscillates because of stray fields at 50 Hz.  By dividing the top trace into the left hand half (red) and the right hand half (purple), and subtracting them to make the lowest trace, the oscillation was removed, leaving a clean pulse.  

The moving electric field made the electrons in the paper-clip move, generating a minute electric current which caused a voltage to appear at the input of the oscilloscope.  The peak voltage was about 20 mV.  The input impedance of the scope was 1 megohm, so the peak current was about 20 nanoamps.

Travelling at 10 cm/second at 2 mm from a paper-clip does not make much of a wave, but a charged particle travelling at almost the speed of light may pass within 10^-10 metre of electrons in a medium.  Each electron passed will jiggle like the pulse above, and will produce a little disturbance of the electromagnetic field.  The picture below gives some idea of the effect, for a particle travelling at 0.5 of the speed of light.  What this simulates is a snapshot of the field disturbances  that have recently been created as the particle travelled from left to right.  Although the disturbances are almost continuous, they are shown as a series of circles for clarity.

The next four pictures represent the effects of particles travelling at 0.7, 0.9, 1.1, and 1.3 of the speed of light (c), respectively.  When the particle travels faster than light, a cone of line is emitted, rather like the conic shock wave produced by a supersonic aircraft, or the waves made by a ship.

The green diagrams represent only snapshots.  The next picture represents a set of images from many different positions of the particle, as if seen by a stroboscopic camera.  The cones are actually produced continuously, so that light spreads forwards (though behind the source) and outwards as the particle progresses.

The next two pictures show waves made by Greylag geese, Anser anser -

How can the particles travel faster than light?  Suppose that they are travelling at 0.9 of the speed that light has in a vacuum, usually denoted by c (why?).  If they pass into a refractive medium where the speed of light is 0.75 of its vacuum speed c, the particles now have 0.9 / 0.75 of the local speed of light, that is 1.2 of the vacuum speed of light..

This light can be used not only to detect particles, but to identify and measure them.  This is possible because the speed depends on the energy and the mass of a particle.  If the energy can be measured separately, and the Cherenkov light gives the velocity, and the mass can be calculated.  A device known as a ring-imaging Cherenkov counter enables the direction and the velocity of particles to be measured electronically.

This light is seldom seen in normal circumstances.  Because cosmic rays are so energetic, they can actually travel faster than the speed of light in air, even though  that speed is almost equal to c.  Huge light detectors are used to capture this Cherenkov light during the night, to help in studies of cosmic rays, whose origin is largely unknown.  Nor do people know how these particles can attain such colossal energies.

The pictures for speeds below the speed of light show that the rings in front of the source are more closely packed than those behind.  The wavelengths are altered by the movement.  Because of this, as the source approaches the observer, she or he will detect more waves per second than in the static case.  After the source has passed, the frequency drops below the static value.  Familiar examples are sirens of police cars and ambulances.  Astronomers use this effect, called the Döppler effect, to measure the speed of stars relative to us, using the shift in wavelength.  They know what the wavelength should be because the atoms in all stars emit light with wavelengths determined by the type of atoms in them.  The patterns of wavelengths can be recognized even after they have been grossly shifted.

If an aircraft approaches at a height of 150 m at 0.99 of the speed of sound, you cannot hear anything until it is almost overhead, because it is almost keeping up with the sounds it makes.  When you do hear it, you will hear all the sounds that you would normally have expected to hear during the approach, piled up into a short and shattering burst of noise.

If the aircraft is travelling faster than sound, the waves never get the chance to propagate in  the normal manner - they come together in a shock wave.  When you eventually hear the sound there is a sharp increase in air pressure, then a decrease to lower pressures, then a return to normal.  At close quarters the sound may be a double bang - further away it is more of a dull boom.

Another effect of motion is that the apparent source is behind the real one, as the circles show.  The motion of waves is always at right angles to the wave-fronts, so the light seems to come from the centres of the circles.  In fact it actually does come from the centres, but by the time we see the light, the source has moved on.  This effect is very noticeable when an airliner passes high overhead - the sound appears to come from a point far behind it.

You get the same effect with rain.  If a small cloud passes over, the rain slopes forward with the wind, and the direction of the rain points back to a place well upwind of the cloud, and not at the cloud.  If you see such an event in the distance, you may see the band of rain sloping upwind from the cloud, but the individual drops are sloping downwind.

A related effect of motion is what happens to light when it reaches the earth.  Because the earth is moving in a circle around the sun, telescopes have to be pointed slightly off the right direction - the stars appear to go round in tiny circles or ellipses during one year.