**WAVES AND THE SUN**

**Electromagnetic radiation**

The Sun emits, not just visible light, but light from all across the electromagnetic spectrum - from radio waves to gamma-rays. These waves all obey the equation

*c = f l*

where *c* is the speed of light (2.998 x 10^{8} m/s),
*f* the frequency, and *l* the wavelength.

If we measure light from an object that is moving towards us, the wavelength of
the light changes from *l* to *l* ( 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*.

The Sun's surface is cool enough to contain some neutral nickel atoms
which give rise to a spectral line at 6768 Å (Note: 1 Å =
10^{-10} m).

If a piece of the surface of the Sun moves towards us at a speed of 50 km/s, then the wavelength of the spectral line is seen to be 6766.87 Å.

**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.

The vibrations arise through the presence of *standing waves*
in the Sun's
interior. The most simple example of a standing wave is a taut string
fixed at both ends.

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 'ends' between which we find the vibrations are the Sun's surface and another surface within the interior of the Sun (the position of which depends on the particular wave being studied).

The waves cause the surface of the Sun to move up and down by small amounts. These movements can be measured and compared to how the Sun would be expected to behave from models.

** give equation for waves?

The Michelson Doppler Imager (MDI) instrument on the SOHO satellite measures these movements by looking for Doppler shifts in the nickel 6768 Å spectral line mentioned above. The movements of the Sun's surface are a lot less than 50 km/s, however, and are typically only around 0.5 km/s.