THE SUN AND WAVES
Waves play a very important role in the Sun. The Sun emits, not just visible light, but light from all across the electromagnetic spectrum - from radio waves to UV, X-arys and gamma-rays. These are transverse waves, like the waves produced with a rope or in water. the direction in which the rope or water moves is at right angles (perpendicular) to the direction in which the wave moves. Sound (acoustic) waves are an example of a longitudinal wave. As the wave moves along it makes the molecules of air move backwards and forwards in the same direction as the wave.
v = f x lambda
where v is the speed of the wave, f the frequency, and lambda the wavelength. The speed is a constant c, the speed of light (2.998 x 108 m/s), for electromagnetic waves. The speed of sound depends on the properties of the medium through which the wave travels.
Doppler Shifts
If we measure light from an object that is moving towards us, the wavelength of the light changes from lambda to lambda ( 1 -v/c), where v is the speed of the object moving toward us. This shift in the wavelength is referred to as a Doppler shift. You'll hear this effect when a car speeds around a race track, towards and then away from you.
Sound waves - Helioseismology
Seismology is the study of earthquakes and is done by measuring the vibrations of the Earth's surface. Helioseismology is a comparatively new field of solar physics (begun in the 1970s) whereby vibrations of the Sun's surface are measured (Helios is the Greek word for Sun).
The vibrations arise through the presence of standing waves in the Sun's interior. The simplest example of a standing wave is a musical instrument, for example a guitar or flute.
The equation describing these waves is
put basic wave equation here
A solution for a string of length l is
y = sin (r pi x / l) * [ a cos (r pi c t/l) + b cos (r pi c t/l) ]
This solution is called a normal mode of vibration of the string. There are an infinite number of these modes corresponding to r = 1, 2, 3, etc.
In the Sun, we get 3-dimensional standing waves.
The waves cause the surface of the Sun to move up and down by small amounts, a fraction of one km/s. We can detect these small motions by looking at the Doppler shift in spectral lines emitted by atoms in the solar surface. These movements can be compared to how the Sun would be expected to behave from standard theoretical models of stars.
This image was produced from observations by Michelson Doppler Imager (MDI) instrument on the SOHO satellite. It shows the difference between the calculated and predicted speed of sound waves, inside the Sun.