intuitive explanation why frequency is fixedby pivoxa15 Tags: explanation, fixed, frequency, intuitive 

#1
Dec1906, 05:31 AM

P: 2,268

From treating light as a wave it is possible using Huygen’s theory to deduce that the frequency of the light will not change whether in vacuum or some other material. I have seen a mathematical proof of it and understand it but is there an intuitive explanation for it? Does it match Maxwell theory of light?
What about this explanation: Light is emitted by an accelerating charge that is also changing direction so after the light is emitted the frequency is fixed but wavelength change depending on the material. This explanation is just like treating light as a mechanical wave. Water waves are generated by a vibrator and if the medium it travels through changes the frequency is the same but wavelength changes. Correct? If so than its as if Huygen is treating light as a mechanical wave. Which is wrong as proved by Maxwell? So frequency is really not fixed according to Maxwell? 



#2
Dec1906, 01:27 PM

Sci Advisor
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The boundary conditions of a wave at an interface can only be satisfied at all times if the incident wave and the reflected and transmitted waves all have the same frequency.




#3
Dec1906, 02:42 PM

P: 2,268

So not only mechanical (i.e. sound, water) but electromagnetic waves also obey the law that frequency is fixed in any material? 



#4
Dec2006, 09:04 AM

Sci Advisor
HW Helper
P: 1,930

intuitive explanation why frequency is fixed
If you tie two strings of differeing mass densilties together, the end of each stilng will oscillate at the frequency of the knot. The same is true for the E and B fields at a change of dielectric constant.




#5
Dec2006, 12:00 PM

Mentor
P: 11,224

http://farside.ph.utexas.edu/teachin...es/node59.html Using Ampere's Law, one can come to similar (but sort of "opposite") conclusions about the magnetic field B: the perpendicular component must always be continuous, and the parallel component must be continuous across a boundary that carries no net surface current. If an electromagnetic wave had different frequencies on the two sides of a refracting boundary, the E and B fields would have to be usually discontinuous at the boundary. 



#6
Dec2006, 03:24 PM

P: 2,268

When applied to E and B fields upon entering two different media, consider the electric fields E1 and E2 in media 1 and 2 respectively. Even though they are different, they must be tied together and oscillate smoothly so from the above analogy must oscillate at a single constant frequency. Same applies for B. 



#7
Dec2006, 03:33 PM

P: 2,268

Could you explain a bit more about how the frequency ties in with this example? Should I be thinking about the E and B wave equations? 



#8
Dec2006, 04:22 PM

Mentor
P: 11,224

[tex]E = E_{max} \sin (kx  \omega t + \phi_0) = E_{max} \sin \left( \frac {2 \pi x}{\lambda}  2 \pi f t + \phi_0 \right)[/tex] You have two waves like this, one on each side of the boundary. [tex]E_1 = E_{1,max} \sin \left( \frac {2 \pi x}{\lambda_1}  2 \pi f_1 t + \phi_{01} \right)[/tex] [tex]E_2 = E_{2,max} \sin \left( \frac {2 \pi x}{\lambda_2}  2 \pi f_2 t + \phi_{02} \right)[/tex] For simplicity, let x = 0 at the boundary so the terms with x disappear. Now suppose [itex]f_1 \ne f_2[/itex]. Can you make [itex]E_1 = E_2[/itex] at all times t, while keeping [itex]E_{1,max}[/itex], [itex]E_{2,max}[/itex], [itex]\phi_{01}[/itex] and [itex]\phi_{02}[/itex] constant? 



#9
Dec2006, 06:48 PM

P: 2,268

So you first proved the electric fields in both media must equal at the boundary for all time.
Then one can see that the wave equation for E at a given location has one variable t. The constant scaling this variable is f. In order to keep both E equal at the boundary for all t, the freqeuncy must be the same for both E (otherwise as t changes the two E will differ). The other constants such as Emax, lambda, thi can be different for each E (note the term [tex]2\pi[/tex]ft will occur in both equations) provided they 'combine' in the end so that both E are equal This would be Maxwell's way of showing that frequency is fixed in any media? So it agrees with Huygen's method by treating light as a water wave. So no matter what sort of wave the frequency will be the same in any media while the velocity and wavelength change. 


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