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There are two kinds of waves. One is mechanical for which the energy is given by the expression 2 m pi2 a2 nu2 . a is the amplitude of vibration and nu is the frequency of vibration. Hence in case of mechanical waves, energy is proportional to the square of the amplitude.

But in case of electromagnetic wave photon concept is introduced as quantum of energy. The energy of thee quantum is given by the expression h nu. Here h is Planck's constant and nu the frequency of radiation. Hence the energy content of each photon is proportional to the frequency of radiation.

But the intensity of radiation is computed by the number of photons per second.

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Q: How do the wavelength and the frequency of a wave determine its energy?
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