Wave Intensity

[victorias]

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Intensity is proportional to amplitude squared because we want to look at the area under the amplitude

I = Power/Area
So if we increase the area, intensity should decrease

Increasing the amplitude means that the area under the amplitude also increases - shouldn't this mean that intensity would decrease? I can't seem to relate this correctly to the idea that intensity is proportional to amplitude squared

 

[bobeanie95]

Intensity is dependent on the energy of a wave, and a wave with a higher amplitude has a higher energy. Therefore, amplitude and intensity are directly related. Remember that Power=Energy/Time so if the energy is increasing then I=P/A will also increase.

In regards to "Area", the area is referring the amount of surface experiencing the energy of the wave (ie. the size of the eardrum someone with a smaller eardrum will experience a higher intensity). It doesn't have to do with the area under the curve.

It might help to think about it in terms of Pressure=F/A. The area is the surface of an object that is experiencing a force F. Likewise, a smaller area corresponds to a higher pressure.