Light Spectrum - Sum of Waves or Collection of Waves

The answer depends on what you mean by "each wave of light." If you mean that you isolate a very narrow ray of sunlight as through a very small hole, then it will contain all the wavelengths. If you mean that you isolate a part of the sunlight using a diffraction grating or prism spectrometer, then it will contain a very narrow band of wavelengths. Maybe you can elaborate on what you mean.

This is a more QM explanation.

The light from the Sun is white light (contrary to popular belief it is not yellow), and contains all visible wavelengthts.

This means, that the light coming from the Sun contains photons of all visible wavelengths (400-700nm).

The human eye is able to detect even one single photon. Now when you look at the direct Sunlight, your eye receives photons of all visible wavelengths (400-700nm), and the cones and rods in your retina are sensitive to these specific wavelength photons. Since in the case of white light from the Sun, all receptors are activated in your retina, you will combine this as white light (it appears yellow to you because of the atmosphere's scattering effect on the photons).

You are asking whether each EM wave has its own frequency, or each EM wave has a combination of different frequency lights.

You are confused because of the classical and QM model of light.

Now the original equations (Maxwell) and model of classical EM waves and light treats light as an EM wave, having a certain frequency, thus a certain energy, and color.

The QM model of EM waves, where a herd of photons build up the classical EM wave, work perfectly together with the classical one.

Each photon has its own wavelength, frequency, thus its own color (our eyes interpret it as color).

The EM waves that make up the white light coming from the Sun are built up by a herd of photons, each photon having its own wavelength (color), and our eyes receptors combine the different photons into a single combined light (in the case of the Sun it is white).

Think about how electromagnetic radiation is generated. Electrons and protons emit photons. The wavelengths of this photons depends from the surrounding temperature, for the protons it depends from the chemical elements (H, He, ...., C). Furthermore it depends from the gravitational potential and the velocity of gas streams. Perhaps this are not all parameters. The spectrum is the sum of all of this photons.

Waves are oscillating energy distributions. One see them then a star is rotating as fast as the magnetic field influence the emitted photons in a way that we can discover a waveform distribution of electromagnetic radiation. From our sun we get a continious flow of photons of different energy levels. They don't have oscillating energy distribution.