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When increasing the intensity of a wave does not lead to ejected electrons, the frequency of the light does. However what does it mean to increase the intensity of a wave rather than just the frequency of it?
Increasing the intensity of the wave increases the amplitude, and thus increases the amount of energy the wave has if light is behaving as a wave. For example, large waves in the ocean(higher amplitude) are stronger and have more energy than small waves(lower amplitude).
basically, the energy of a photon is related to the frequency and the intensity is related to the number of photons. Therefore, when we talk about energy strength of something, we are talking about the frequency.
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