So, in school, I have been taught that $I$ is proportional to $A^2$.
However, when I look at the equation $E = h\cdot f$, I see the frequency has an impact too on the intensity!
Now, if a sound wave has a higher frequency, does that mean the intensity is higher? (NOTE: I am NOT asking about if the pitch will be higher.)
Best Answer
No, frequency does not have an impact on intensity.
If you treat sound waves from a Planck view, the energy of each quant (phonon) is neglectably small: such low-frequency waves behave totally as classical waves, which are made up of zillions of coherent quanta. Changing the precise number (for a given frequency) changes the intensity, obviously. Changing the frequency while keeping the intensity constant means the number of phonons will have to change as well, but you don't notice that since there are no usefully observable processes with such single phonons.
For light, or even gamma-radiation, I can't quite argue this way because here quantum processes are very much relevant; but still intensity and frequency are orthogonal quantities. You can have a gamma source with extremely low intensity, such that on average only a photon per second is emitted. A visible-light source at the same intensity will send out far more photons, but again that doesn't link frequency and intensity, it's just that quantisation involves both.