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The shorter the wavelength, the more energy. In terms of visible light, this means that violet light has the most energy. Of course, there are invisible frequencies that have even more energy.

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Not all waves carries electromagnetic energy, what you call "light energy". Sound propagates in materials like a wave and in general relativity even gravitational wave exists..

If we limit to electromagnetic waves, the quantum field theory tells us that the power P (energy per second) carried by an electromagnetic wave is equal to

P=n h f

where n is the number of photons carried by the wave per second, h is the Plank constant (a universal constant appearing in all quantum theories) and f the wave frequency. The term Eq=h f is also the energy quantum of the wave, that is the energy of one photons.

Thus we have essentially two ways to increase the wave power: either increasing the number of photons travelling through the wave front per second or increase the frequency f, that is increasing the energy of one photon. The wavelength is inversely proportional to the frequency, thus higher the frequency lower the wavelength.

If we compare waves carrying the same photons flux (number of photons per second) the more energetic wave (the wave carrying more energy per second) is the wave having higher frequency.

This is why high frequency waves like gamma rays conveys a lot of energy even if they have a small number of photons.

The different energy of the single photon has also an important impact on how the wave interact with matter.

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