Frequency: Electromagnetic waves

[ravikannaujiya]

Are the angular frequency in electromagnetic waves and frequency of a photon characterise the same physical quantity? I know that these come under two different theory, but I want to know whether these names (angular frequency of em wave and frequency of photon) mean the same physical quantity or they mean different physical quantities. Thanks.

 

[RUber]

Angular frequency is normally in radians per second, i.e. $\omega = 2\pi f$ and frequency (f) is normally given in hertz, or cycles per second.
Otherwise, I believe there is no difference in the meanings of the frequencies of EM waves and photons.

 

[ravikannaujiya]

Thanks for replying. I also think that there is no fundamental difference between them. But, I have asked the question because in Electromagnetic theory, energy of light depends on the amplitude of the wave but not on the frequency, while energy of light depends on frequency in quantum theory. So, I thought the angular frequency of em wave (which energy is independent of) and frequency of photon (which define energy of light) describe two different things or both have different meaning in different theory.

 

[Drakkith]

But, I have asked the question because in Electromagnetic theory, energy of light depends on the amplitude of the wave but not on the frequency, while energy of light depends on frequency in quantum theory.

Hmmm. I was under the impression that the energy of a classical EM wave increases with both increasing amplitude AND increasing frequency.

 

[ravikannaujiya]

That's true for mechanical waves.

 

[davenn]

Drakkith is correct, its also true for EM

have a search on the increasing energy of EM freq at IR, visible light, UV, x-ray and gamma radiation and you will see the increasing electron volt valuesDave

 

[tech99]

Drakkith is correct, its also true for EM

have a search on the increasing energy of EM freq at IR, visible light, UV, x-ray and gamma radiation and you will see the increasing electron volt valuesDave

My understanding is that the energy of a wave is always dependent on its amplitude (energy proportional to amplitude squared). Although the energy of a light beam is in the form of waves, it is contained in small packets, the quanta. As the frequency is raised, the packets each contain more energy, so the light becomes granular in nature. For some purposes, such as triggering chemical reactions and electron emission, it is the energy in a packet which is important.

 

[ravikannaujiya]

Drakkith is correct, its also true for EM

have a search on the increasing energy of EM freq at IR, visible light, UV, x-ray and gamma radiation and you will see the increasing electron volt valuesDave

read page number 488 third line from above of Sear and Zemansky's University Physics 13th edition. Let me send a screen shot of the said paragraph.

 

[davenn]

unreadable ... what's your point ?

 

[ravikannaujiya]

First its not my point its something conceptual that the book says...

"Electromagnetic waves turn out to be a bit different. While the average rate of energy transfer in an electromagnetic wave is proportional to the square of the amplitude, just as for mechanical waves, it is independent of the value of ω ."

 

[jtbell]

Electromagnetic theory, energy of light depends on the amplitude of the wave but not on the frequency, while energy of light depends on frequency in quantum theory.

In quantum theory, the energy per photon depends on frequency. A classical electromagnetic wave corresponds to many many many many ... many many photons.

When you increase the amplitude of a classical electromagnetic wave but keep the frequency the same, the energy carried by the wave increases. The energy per photon stays the same, and the number of photons increases so as to increase the total energy.

When you keep the amplitude of a classical electromagnetic wave the same, but increase the frequency, the energy carried by the wave stays the same. The energy per photon increases, but there are now fewer photons, so the total energy stays the same.

 

[Drakkith]

When you keep the amplitude of a classical electromagnetic wave the same, but increase the frequency, the energy carried by the wave stays the same. The energy per photon increases, but there are now fewer photons, so the total energy stays the same.

Interesting. I thought the energy of the wave increased with increasing frequency as well as amplitude. But apparently not!

 

[jtbell]

The average energy flux (J/(m²·s)) in an electromagnetic wave, averaged out over the oscillations, is $$\langle u \rangle = \frac{1}{2}\epsilon_0 c E_\textrm{max}^2 = \frac{1}{2 \mu_0} c B_\textrm{max}^2$$

 

[ravikannaujiya]

so, I think we are settled on that energy of light depends on amplitude in EM theory and on frequency in quantum theory. Now, please, could anyone tell me whether frequency of light in EM theory is same as frequency of light in quantum theory or not.

 

[Drakkith]

so, I think we are settled on that energy of light depends on amplitude in EM theory and on frequency in quantum theory. Now, please, could anyone tell me whether frequency of light in EM theory is same as frequency of light in quantum theory or not.

As far as I understand it, the frequency of an EM wave in classical physics is the same as the frequency of a photon, so yes.

 

[ravikannaujiya]

thank you guys... :)