Waves are a form of energy. They include electromagnetic waves and sound waves. Electromagnetic waves are the visible light waves and the microwaves that you use every day. The sound waves are just what they are the way sound transfers in a volume.
The electromagnetic spectrum is the range of all the possible frequencies of electromagnetic radiation. This includes all visible light infrared light, microwaves,X-rays, and gamma rays. The way a we've is measured is using frequencies. These are the different levels of vibration that take place in a wave. For example a gamma ray has a much higher frequency than a ray of infrared light, because the distance between the peak of the waves are much greater in a gamma ray than in a ray of infrared light.
Sound waves are the oscillation of pressure through the atoms and molecules of matter such as a solid, liquid, or gas. It like electromagnetic waves is composed of a group of frequencies usually measured in Hertz. The higher the measure of Hertz the higher the pitch. As many older people can confirm sometimes very high or very low pitches can be hard or impossible to hear by the human ear.