Wave Energy: Amplitude and Frequency

[UMICHPremed]

Hey everyone,

It would be great if someone can clarify this...

So the total energy contained in the wave is proportional to square of its amplitude; however, in calculations, we use frequency to calculate the energy (E = hf). Frequency is a representation of dispersal of the total energy in the wave and its a measure of intensity. Why is it used to calculate energy and why is it valid?

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[Phantastic]

E=hf defines the energy of a single photon.

Take a look at the photoelectric effect to understand the difference between intensity of the light and the energy of each individual photon.

The energy of a single photon and the intensity of the EM wave aren't related as far as I know...

 

[UMICHPremed]

For electromagnetic radiation in general, E = hf is used to calculate energy. Not just for a single photon. Yes, I have looked over the photoelectric effect before. This is another facet of the discussion.

I think I got it.. it seems like for transverse waves and longitudinal waves energy is measured by amplitude, but for transverse waves frequency is used in calculation (i.e. relative energy differences of visible, uv, and infrared E=hf). However, for longitudinal waves like sound waves (amplitude is used to measure energy and intensity, while frequency only measures pitch)...

 

[Phantastic]

For electromagnetic radiation in general, E = hf is used to calculate energy. Not just for a single photon.

If the EM radiation is monochromatic, this is the case.

I think I got it.. it seems like for transverse waves and longitudinal waves energy is measured by amplitude, but for transverse waves frequency is used in calculation (i.e. relative energy differences of visible, uv, and infrared E=hf). However, for longitudinal waves like sound waves (amplitude is used to measure energy and intensity, while frequency only measures pitch)...

Indeed, I've only ever used the frequency to determine the energy when dealing with transverse waves. Sorry, I think I misread your original question.

 

[phltz]

Energy is proportional to the square of the amplitude in classical mechanics. This is generally the calculation we'll use for sound waves, water waves and the like.

For smaller systems, though, quantum mechanics becomes relevant. It turns out that energy is _quantized_. In the case of electromagnetic waves, energy is quantized into photons. One photos has an energy given by E=hf. Any time we see Planck's constant in a calculation, we should immediately realize we're talking about a situation where quantum mechanics is at play.

It's worth noting that if we had a lot of coherent monochromatic photons moving together (as in a laser), it'd still be accurate to say that the overall intensity would be proportional to the amplitude of the electric field oscillations (we could alternately use the magnetic field, of course).

Although it's beyond the scope of the MCAT, other waves are also quantized if one looks at them on a small enough scale. Vibrational waves are quantized into packets of energy called "phonons", which also have an energy given by E=hf. These become relevant if you want to analyze the physics of, say, IR spectroscopy.

 

[UMICHPremed]

Makes sense, thanks!

 

[Phantastic]

You just blew my f***** mind, man. 👍

 

[destroythemcat]

Phltz you really seem to know what your talking about. On a related topic, i was wondering if you could help me out. When light goes from a less dense medium to a more dense medium, frequency stays the same, but Velocity increases. If frequency stays the same then energy E=fh cannot change, but when a denser medium absorbs light and then reemits it the photon can loose energy, and if energy decreases, how does frequency stay constant?