Intensity & Energy

[Majik]

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Intensity = Power/Area;
(Discussed in the Sound Chapter of TPR)

Also, I recall reading that Intensity is also related to different variables:
- It's proportional to velocity
- It's proportional to the square of frequency
- It's proportional to the square of amplitude
- It's proportional to the density of the medium
(Discussed in the Wave Chapter of EK)

Are these the same thing?

Also, if I were looking to find the energy of a wave, could I resort to changes in intensity to figure out how energy changes. For example:

Intensity = Power/Area; Power = Work/time therefore:
Intensity = Work/(Area)(time) (Work is a form of Energy)

Provided everything above is true and both intensities are essentially the same thing, then why does this contradict the other equation for energy:

E=hf. Here, doubling frequency implies that the a double in energy. Above, doubling frequency, quadruples intensity. If intensity quadruples, that would imply energy increased by a factor of 4. Could anyone explain why these two don't add up?

Am I doing something wrong here?

 

[Majik]

Oh wait, I figured it out.

Frequency = 1/T, so doubling frequency halves time. Doubling frequency Quadruples Intensity.

Intensity = Power/Area = Work/(time)(Area)
Rearranging: Intensity x Area x time = Work

(4I)(A)(t/2) = 2W so Work (Energy) doubles.