I get confused when I read that the Energy of wave in classical mechanics is correlated to the amplitude E ~ A^2 (pls. point me to a doc which shows that, couldn't find any exact formula on internet), but then when we are talking about atoms,photons,electrons they say it is dependent on the freq. i.e. E = hf. Here is how I do my interpretation on those explanations. If I imagine a ocean wave (similar to sound wave) I will expect that I will measure the energy of the wave impacted on specific area. From this follow that I'm looking at the Intensity which is defined as Power over area i.e. I = P/Area.. We know that Power is Work done over time i.e. P = W/t, Work is the Energy dispensed to do a job i.e. W = F*d. Following this line of thought I then figure out Energy transported from a wave is correlated i.e. depend on E ~ Amplitude * velocity * area ? The bigger any of them more energy is transferred. Making logical jump for the small world that velocity is synonymous for frequency... E ~ Amplitude * frequency * area ? ... we conclude then that when doing photo-electric experiment we are expecting that the energy transferred by the "impact wave" (remember we dont know yet, we are speculating that light is a wave, still) will be dependent on the Amplitude in our case brightness of the light. So when later we measure the fleeting electrons off the metal we would expect that when we increased the the brightness(Amplitude) we would get faster electrons (more Energy), but we don't. But when the scientists changed the color(freq) of light they saw that they got their faster electrons. This then proved that the Amplitude does not have impact on the velocity of the electrons (which was expected from classical mech) i.e. kinetic-energy, but only on the number of the electron emitted (if emitted at all) i.e. Intensity of the output! Did I made the correct assumptions and explanations. I'm looking for the connection of disregarding the Amplitude. I know we are talking about specific electrons, but their wave quality still implies amplitude right? Or is it because the amplitude is bit wave amplitude , but probabilistic ? Still in 1900+ they didn't knew that , yet.