No, not all electromagnetic waves have the same speed in a given medium. The speed of electromagnetic waves depends on the properties of the medium through which they are propagating.
In a vacuum, all electromagnetic waves, including visible light, radio waves, microwaves, X-rays, and gamma rays, travel at the same speed, which is approximately 299,792,458 meters per second (often rounded to 300,000 kilometers per second), denoted by the symbol "c." This speed is commonly referred to as the speed of light in a vacuum.
However, when electromagnetic waves pass through a material medium, such as air, water, glass, or any other substance, their speed can be different from the speed of light in a vacuum. The speed of electromagnetic waves in a medium is determined by the medium's refractive index, which is a measure of how much the speed of light is reduced when it enters that medium.
Different materials have different refractive indices, which means electromagnetic waves will travel at different speeds through different media. For example, light travels slower in water or glass than in air. The refractive index of a medium determines how much the speed of light is reduced as it passes through that medium. The relationship between the speed of light in a vacuum (c), the speed of light in a medium (v), and the refractive index (n) of the medium is given by the equation v = c/n.
In summary, while all electromagnetic waves travel at the same speed in a vacuum (the speed of light), their speeds can vary when passing through different materials due to the refractive index of the medium.