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When the experiment changed the intensity of the light on the metal, it is only changing the amount of photons in the light. Lower intensity means less photons and thus dimmer light. Electromagnetic wave does not behave the same as sound wave or ocean wave. When we increase the intensity of an EM wave the frequency does not change. In order to increase the frequency, the experiment needed to a completely different type of EM wave that has higher frequency.
The electromagnetic wave being used did not change hence the frequency did not change. By increasing the intensity you are simply increasing the number of photons being directed in the light towards the surface.
Using the wave model of light, increasing intensity of light increased the amplitude of the wave, not the frequency. However, in the quantum model of light the intensity of light corresponds to number of photons (i.e. doubling the brightness doubles the number of photons but has no effect on frequency of each individual photon).
Another important aspect to remember is that each photon interacts with only one electron, and furthermore, if you increase the intensity of the light and if you have enough energy per photon, then more electrons would be emitted.
I think intensity is basically a measure of how many photons are available. With intensity, it usually correlates to the wave model of light, but frequency typically correlates with the photon model of light. Frequency is increased when wavelengths are shorter, but that has no correlation to the amplitude of the wave. For the most part, I think amplitude of the wave is related to the intensity of light.
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