intensity mechanical vs electromagnetic waves/amplitude vs frequency

[km1865]

So i understand that intensity is related to the frequency^2 and the amplitude^2 for BOTH electromagnetic and mechanical waves, right? But is there is NO RELATIONSHIP between amplitude and frequency just by themselves ? Im getting confused on the factors that cause the intensity to change for EM/ mechanical waves? So basically for EM waves, we can say E=hf and energy is directly related to frequency and for mechanical waves E is proportional to the amplitude squared.. but how can we relate the intensity of the two? And I also ran across a question once about the photoelectric effect asking which of the following would increase the NUMBER of electrons ejected from a metal surface, Increasing the area and the intensity of the incoming light were the correct answers, I got this right but looking back at it Im a little confused since the definition of Intensity is P/A so increasing area should decrease intensity right? can someone just explain why the above answer was correct. Im clear on why the frequency WOULD NOT cause more electrons to be ejected but rather increase the KE of each electron.... THANKS

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[costales]

More surface area exposes more electrons to be ejected. More intensity gives you more photons to knock them off with.

 

[docntrainin]

More surface area exposes more electrons to be ejected. More intensity gives you more photons to knock them off with.

Adding to this, higher frequency translates to higher kinetic energy

 

[costales]

But is there is NO RELATIONSHIP between amplitude and frequency just by themselves ? I

Say you have a rope. How often you shake the rope (frequency) has nothing to do with how hard you yank the rope up and down (amplitude).