Your equation is true of electromagnetic waves. Other waves (say, waves in water) have a different (and lower) traveling speed. But the frequency times the wavelength is the speed at which the pattern moves. WHY electromagnetic waves travel at the speed of light is not knowable--they just are observed to do so.

https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality

there is no spoon

Because the wavelength is c divided by the frequency.

Same reason the speed of a car driving in a sine wave will be its frequency multiplied by its amplitude.

You're basically just asking "why does EM radiation move at the speed of light". To which the answer is: "it just does".

You're multiplying a rate (/s) by a distance (m) so you get a speed, m/s.

Infinity in a Reimann universe is equivelant to -1/2 +- sqrt(1/12)

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c=nu*lambda; nu=frequency and lambda=wavelength
The unit of frequency is cycles per second and that of wavelength is a displacement. Therefore, dimensional analysis provides you with displacement per second. Also, many electric and magnetic fields travel at speeds different from the speed of light, both faster and slower. Faster ones make it out of black holes, which ones depends on the escape velocity of black holes. The question you want to ask is how can we know theoretically that the matter eaten by the black hole conducts, and well, which we know from the electric and magnetic fields that escape from it near the axis of rotation.

quantum physics is stupid. waves, quants, photons. blah blah. it doesn't make any sense. physics in this regard is a giant bloated mess full of convenient mathematical tricks, but there is actually no real understanding, because no real observation can take place at this scope.

C The speed of light is used in many formulas as convenient shorthand for a bloody big number. The bigger the number the harder it is to prove it wrong and the closer to actual it will get the maths. Einstein used it to jump over the true speed of light .

Quantum theory is just that and draws a lot of funding for university layabouts to spend on themselves . Little will ever be achieved by quantum theory . For example it can be proved in quantum mechanics that black is equal to white with a 99.99% probability. Now if that's not stupidity extreme then I'll eat my own balls.