I have been thinking about what would happen if by chance the photons collided with each other. I heard once that electromagnetic waves pass through each other without any interference.
I wanted to know if I am correct?
Does the collision produce sound?
Photon photon interactions are very rare below the rest mass of twice the electron.
The quantum mechanical feynman diagram of two photons interacting, from which the probability of interaction can be calculated: has four electromagnetic vertices, i.e. (1/137)^1/2 for the amplitude, and when squared as it multiplies the integral for the probability, the number becomes miniscule, so photon photon interactions are very rare.
Please note it is very important to understand that two photons can and sometimes do interact, through higher order processes.
The photons can interact through higher-order processes. As pointed out in the comments (and I hope I'm getting this right), there is a (quite small) probability amplitude for two photons to get absorbed in, and two photons be emitted by, e.g. an fermion-antifermion virtual pair (which is the leading contributor to the combined amplitude of all such processes).
What would the collision of two photons look like?
You are saying that EM waves pass through each other without any interactions, in reality, this only works in the approximation of very dim light. This statement is based on light's (and Maxwell's equations) linearity and the superposition principle. If you increase the frequency or intensity, you would observe nonlinear behavior.
The key aspect of the superposition principle is linearity, that is, the fact that Maxwell's equations are linear. If you consider electromagnetic radiation in a certain material, it is well-known that for intense enough radiation the polarisation becomes non-linear, and you enter the realm of nonlinear optics.
Why are light rays able to cross each other?
It is very important to understand that interference (the phrase you are using) and interactions are different phenomena with light. I do believe you really meant interactions. For interference, please see a very good example, the double slit experiment.
So when as you say we use phrases like "two EM waves pass through each other without interacting", we usually refer to relatively lower energy levels or intensities, but in certain cases, we enter the realm of higher order non-linear processes, where the interaction is possible.
