If you have two waves which have the same frequency, is it implied then that they have to have same wavelength? Will there be a scenario when two waves with same frequency have different wavelength?
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4 Answers
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For example, in a birefrigent medium (https://en.wikipedia.org/wiki/Birefringence), the wavelength depends on the polarization, so two waves in the same medium and with the same frequency but different polarization can have different wavelengths.
answered Aug 18, 2018 at 14:05
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If you have two waves which have the same frequency, is it implied then that they have to have same wavelength
Nope nope nope. That's only when you're assuming that they're travelling through the same medium and have the same polarisation.
Here's a simple counter example: Humans identify light with a frequency of $\approx 450\ \rm THz$ as red light. That's the way our eyes work. We know that the frequency of light remains the same when it travels from one medium to another, so when I'm underwater, the wavelength of the red light I see is about $450\ \rm nm$, but when I'm in a vacuum, the wavelength is about $600\ \rm nm$. Same colour observed, same frequency, but different wavelengths.
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1$\begingroup$ Well the observation happens at the back of the eye, so the medium is the same before it hits the retina. I understand what you want to say, but your example does not show it. $\endgroup$– lalalaCommented Aug 18, 2018 at 14:00
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$\begingroup$ @lalala I'm not talking about what's going on inside the eye. I just wished to make the point that our eyes distinguish between frequencies, not wavelengths. I mentioned eyes only after some deliberation about possible misinterpretation, because I wanted to make it possible for people to imagine looking at things underwater. $\endgroup$– user191954Commented Aug 18, 2018 at 14:05
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$\begingroup$ The only point this shows is that when light goes from one medium to another then the frequency stays constant (which is a very inportant point) $\endgroup$– lalalaCommented Aug 18, 2018 at 14:10
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$\begingroup$ @lalala That is an important thing to mention; I'll edit my answer to include that. $\endgroup$– user191954Commented Aug 18, 2018 at 14:12
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If they have the same speed, then yes, they will.
frequency = cycles/time
wavelength = distance/cycle
So by simple algebra, speed = frequency * wavelength
If the waves have different speeds, they will differ in wavelength though.
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$\begingroup$ In the future, you may want to use MathJax. It's significantly less cumbersome than writing full definitions; you get to use conventional symbols. $\endgroup$– user191954Commented Aug 18, 2018 at 17:01
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I am an amateur that conducted an experiment on this very topic. Yes, there are situations where the frequency remains constant but the wavelength changes. This will affect the speed at which the wave travels. The wavelength contracts when it passes through a medium (note: I have not tested all mediums) Here’s a link to my experiment: Is the decrease in wavelength proportional to the reduction in speed? The contraction appears to be proportional to the reduction in speed. The test was simply to place a diffraction grating above water and measure the separation. Then perform the same test under water and measure. There was an obvious reduction in wavelength, but the color seemed to remain the same. This indicated that the frequency remained constant. Once again, please note this was an amateur experiment done in my garage, but I think it holds water, pun intended.
