My problem is: How can I resolve these following ideas?
Energy of photons in an EM wave is proportional to the frequency of the wave
Intensity of an EM wave is proportional to the energy that is incident an area per unit time
Intensity is proportional to the number of photons incident on an area per unit time
Based on reviewing previous physics stack exchange questions (such as Relation between frequency and intensity of light):
Intensity = I = Nhν/A if N is the monochromatic photon emission rate (photons per second), ν is the frequency of the photons, and A is the area these photons are hitting.
The above equation makes sense to me.
However, I'm being told that intensity of an EM wave is not related to the frequency of the wave because "light intensity is a wave-like property that depends on the number of photons hitting a certain area per unit time. Conceptualizing it into the units of power, the Joules component refers to the kinetic energy of photons (1/2 * mv^2). Since light travels at the same speed in a given medium, regardless of frequency, each individual photon contributes equally to energy, and thus to intensity".
But if there are two waves with equal numbers of photons incident on an area per unit time, but one wave has greater frequency, then wouldn't the wave with greater frequency have more energy incident on the area per unit time?
Can I resolve my confusion by using (energy = 1/2 * mv^2)?
Thank you for any help in understanding this!