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This question already has an answer here:

Since the frequency of an electromagnetic wave does not change during refraction but the velocity changes, the wavelength must therefore change. But why doesn't the frequency change in the first place? I heard answers like that frequency is the property of the source but wavelength is not. Even of this is the right answer explanations are not adequate.

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marked as duplicate by garyp, Jon Custer, M. Enns, Javier, John Rennie electromagnetism May 25 at 6:35

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    $\begingroup$ Because the field has to be continuous at the border. If the frequencies were different, both sides would get out of phase. $\endgroup$ – Javier May 24 at 14:20
  • $\begingroup$ It's also a fact that the source determines the frequency. Even when light speeds up or slows down as it encounters various media, this is still true. $\endgroup$ – David White May 24 at 15:59
  • $\begingroup$ The answer to your question will probably also answer the Physics Stack question of how LIGO's splitter mirror can put out two frequencies. How Does LIGO’s Splitter Mirror Cause Two Different Frequencies When a GW is Present? $\endgroup$ – Gary Godfrey May 24 at 19:10
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Here's a qualitative argument. A wave propagates in space and time, but the boundary is a barrier in space rather than a barrier in time. Hence the spatial part of the propagation will change, but the time part will not.

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Think of people in a stadium doing "the wave." You know it's your turn to go because the person next to you went. There is a cause-and-effect relationship which exists at a certain moment in time, hence the time variation of the wave is always the same. The same thing happens with Newton's laws for a wave on a violin string: one element of mass makes a force on a neighboring element of mass.

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You can think of an electromagnetic wave as the ticks of a clock. The clock ticks at a constant rate, and the wave peaks travel away from the clock, each tick corresponding to a wave peak.

If you could stand next to the train of waves as it goes by, and count how many pass you per nanosecond, it must necessarily be equal to the number of ticks per second emitted by the clock -- otherwise ticks would be getting lost (or gained).

Of course, this depends on your own clock running at the same rate as the clock at the source of the waves. If your own clock is running slower, so your measured nanoseconds are longer, then you will count a larger number of wave peaks per nanosecond than would be counted using the clock at the wave source.

As you probably have read, time runs slower the deeper you go into a gravitational well (e.g., toward a star). In that case, an electromagnetic wave falling toward the star will gain frequency as it falls. To an observer deep in the well, the number of wave peaks passing per nanosecond will be increased compared to the number of ticks per nanosecond measured at the "clock" (the source of the waves). Conversely, if the source is deep in the well and you are far away, the waves will pass you at a rate that is reduced compared to the clock rate you would measure at the source. This difference in the rate of time is a major component of the time/space distortion we call gravity.

During refraction light moves slower, but the number of ticks/waves per nanosecond can't change (if gravitational time dilation doesn't occur). The only way that light can be slower but carry the same number of wave peaks per nanosecond is for the peaks to be closer together: that is, for the wavelength to be shorter, in the refractive medium.

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You can think of an electromagnetic wave as the ticks of a clock. The clock ticks at a constant rate, and the wave peaks travel away from the clock, each tick corresponding to a wave peak.

If you could stand next to the train of waves as it goes by, and count how many pass you per nanosecond, it must necessarily be equal to the number of ticks per second emitted by the clock -- otherwise ticks would be getting lost.

Of course, this depends on your own clock running at the same rate as the clock at the source of the waves. If your own clock is running slower, so your measured nanoseconds are longer, then you will count a larger number of wave peaks per nanosecond than would be counted using the clock at the wave source.

As you probably have read, time runs slower the deeper you go into a gravitational well (e.g., toward a star). In that case, an electromagnetic wave falling toward the star will gain frequency as it falls. To an observer deep in the well, the number of wave peaks passing per nanosecond will be increased compared to the number of ticks per nanosecond measured at the "clock" (the source of the waves). Conversely, if the source is deep in the well and you are far away, the waves will pass you at a rate that is reduced compared to the clock rate you would measure at the source. This difference in the rate of time is a major component of the time/space distortion we call gravity.

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