wave frequency and energy

[wormboge]

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Why is frequency of a wave proportional to energy squared?

 

[AdaptPrep]

Hi, wormboge--

Where did you read that/what was the context? E = hf (energy of a wave is equal to Planck's constant times frequency); nothing is squared in this.

However, the energy is proportional to the amplitude squared.

I may be missing something though...

 

[wormboge]

I have been looking into this, and believe it is from the equation, I = (1/2) p w^2 A^2 v In that case intensity is proportional to angular frequency squared, and of course, energy and intensity are directly proportional from other equations.

So, how does this square with the notion that E=hf? How can energy be proportional to frequency in that case, and in the prior paragraph, energy is proportional to angular frequency squared?