Why do all electromagnetic waves travel at the same speed when travelling through vacuum? What does my teacher mean when he says that all electromagnetic waves travel at the same speed when travelling through a vacuum? If you may, please answer as simple as possible.
 A: Electromagnetic waves include visible light, radio waves, X-rays, and so on. What distinguishes these different bands of light is their frequency (or wavelength). But what they all have in common is that they travel at the same speed in vacuum.
The reason for qualifying 'in vacuum' is because EM waves of different frequencies often propagate at different speeds through material.
The speed of a wave $c$, its wavelength $\lambda$ and frequency $f$ are all related according to $c=\lambda f$. So if $c$ is the same for all EM waves, then if you (say) double the frequency of a wave, its wavelength will halve.
A: Assume you are walking down the road. You carry a little stick with you. Just for fun you decide to wiggle the stick rhythmically up and down at the rate of one up/down wiggle per second (you are a bit of an olympic expert at stick wiggling so it's very accurate and reliable). Your stick wiggling is at 1Hz. The speed at which you walk down the road is not related to the rate at which you wiggle the stick. You can walk down the road at any speed you like and still wiggle at 1Hz.
Have you got it now ?
The speed of transmission of an e-m wave is not related to the frequency/wavelength.
A: Not true. Bad analogy. First, in your last sentence you're using frequency and wavelength synonymously, which they're not. Frequency is the (oscillation rate) in a photon particle. Like the waving of the stick, it's frequency is constant. But wavelength is a measure of frequency within the constraints of speed. If frequency is a constant, and speed changes, then the wavelength must change. So, frequency isn't affected by speed, but wavelength is. The stick example shows the frequency constant, but not wavelength. A rollercoaster track example shows the wavelength constant. If a rollercoaster slows down, it still requires it to move through the same path to get to the next crest. It'll take more time to get there, but the wave is still the same shape and distance. But in order for this to work, it's frequency or energy decreases. in the wave particle world, this doesn't happen. Therefore, the rollercoaster example shows us the wavelength as a constant only for theoretical purposes, but doesn't work in the natural wave particle world. Only a particles energy or frequency is constant. This dictates that speed and wavelength can change.
With that established. Let's look at the scenario of photons traveling through a vacuum. In a vacuum, there is nothing to disrupt the speed. If the speed is constant and we have already established the frequency is constant, then the wavelength of that particle is also a constant.
Now if we introduce matter. This causes the particle's speed or trajectory, or both to be altered. Altering the speed will change it's wavelength. Altering it's trajectory will cause it's wavelength to go to zero in that direction. In both instances, energy is transferred and released, which gives rise to the idea that a photon is a particle. But at the same time, once it is free to travel uninhibited again in a vacuum, it reverts back to it's same wavelength and speed, which is characteristic of a pure wave.
This concept of a photon being a wave, is why we believe it has to have the same speed in a vacuum. The simple answer is that we don't really know why they all travel at the same speed. All we know is that this is a characteristic of a wave form of energy. Just like mass is a characteristic of a particle. It just is.
