Final answer:
Electromagnetic waves can propagate through both matter and a vacuum, unlike mechanical waves which need a medium. They are characterized by a constant speed of light and vary in wavelength and frequency across the electromagnetic spectrum, determining their energy and applications.
Step-by-step explanation:
Electromagnetic waves differ from other types of waves in that they can travel through both matter and a vacuum, which is a property not shared by mechanical waves like sound which require a medium to propagate. This unique ability is due to the fact that electromagnetic waves consist of oscillating electric and magnetic fields, and they do not rely on interacting with atoms or molecules to propagate. Electromagnetic waves are also all characterized by a constant speed - known as the speed of light - which is approximately 300 million meters per second in a vacuum.
The electromagnetic spectrum encompasses a broad range of waves with varying wavelengths and frequencies, from very short-wavelength gamma rays to long-wavelength radio waves. Differences among electromagnetic waves, such as their applications and interactions with matter, are determined by their wavelength (or equivalently frequency) and the corresponding energy; shorter wavelengths correspond to higher energy.
Furthermore, electromagnetic waves exhibit wave-like characteristics that can be mathematically represented using sine or cosine functions, including amplitude and frequency. Despite these similarities with other wave types, the capability to transmit energy through a vacuum is a distinctive attribute of electromagnetic radiation. This allows for a variety of applications, from radio communications to medical imaging.