# Frequency: Electromagnetic waves

1. May 14, 2015

### 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.

2. May 14, 2015

### 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.

3. May 14, 2015

### 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.

4. May 14, 2015

### Staff: Mentor

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

5. May 14, 2015

### ravikannaujiya

That's true for mechanical waves.

6. May 15, 2015

### 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 values

Dave

7. May 15, 2015

### tech99

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.

8. May 15, 2015

### ravikannaujiya

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.

9. May 15, 2015

### davenn

10. May 15, 2015

### 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 ."

Last edited: May 15, 2015
11. May 16, 2015

### Staff: Mentor

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.

12. May 16, 2015

### Staff: Mentor

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

13. May 16, 2015

### Staff: Mentor

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

14. May 17, 2015

### 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.

15. May 17, 2015

### Staff: Mentor

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.

16. May 17, 2015

### ravikannaujiya

thank you guys... :)