Energy/Intensity of Electromagnetic Waves vs Mechanical Waves

[ap594]

So, I understand the basics of mechanical waves and the equation I=w^2*A^2*v*p and I understand the basics of electromagnetic waves and the equation E=hf. In EK1001 physics, they describe the energy of a mechanical wave as being proportional to the intensity and, thus, is increased by a factor of 4 if the frequency is doubled (b/c w=2*pi*f). And, the frequency of an electromag. wave increases by 2 if the frequency is doubled because E=hf. I understand all of that. But, then it describes the intensity of two constructively-interfering waves (of the same amplitude) as 4x the original intensity because the amplitude goes up. Does I=w^2*A^2*v*p apply to both of these waves? Or is intensity something different than energy? I'm just a little confused where the A^2 being proportional to I came from. If I don't make sense, let me know; I'm a little tired 😴.

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[EpicBearMan]

When two waves of equal amplitude constructively interfere, the amplitude of the combined wave is twice that of the original wave.

From the equation, I=w^2*A^2*v*p, you can see than when amplitude doubles, the intensity increases by a factor of 4.

Edit:

Also, photon energy is not the same thing as intensity.