11. WAVELENGTH CHANGE IN DOPPLER SHIFT

Wavelength change is described with Doppler Equations below in physics.

Doppler Shift and Wavelength Change
Frames are moving away  from each other	Frames are approaching  each other

As the station on the mountain is motionless relative to the transmitter, the wavelength of the signal coming to it will not change and it will receive the signal at λ₀. But we see that the wavelength changes for the planes, which are in motion relative to the transmitter. We see the amount of this change in the equations above. I’d like you to look at it more carefully. On the top of the fraction bar in the equations, you can see “c+v” in the equation on the left and “c-v” in the equation on the right. What do you think they are? What do they describe? Aren’t they just smiling at you? Can you hear them? “We are the speeds of the signals going to the planes from the transmitter. We are the speeds of the signals going to the planes from the transmitter.”

Please notice the huge flow of information happening all of a sudden. You are now witnessing this huge information transfer. Even though the equations above have been in the hands of scientists for more than a hundred years, they couldn’t understand that they indicate speeds of signals. It is impossible to understand without having (c+v) (c-v) mathematics. 

The equations above tell us the following in a nutshell: If the signal is traveling to a target that is in motion, the original wavelength of the signal changes during the emission of the signal. The rate of this change is insomuch as “the speed of signal emission/the speed of light constant”. And the speed of signal emission is determined by the difference in speed between the source of the signal and the target of the signal together with the speed of light constant.

λ₀ – Factory Setting of a Wavelength

The original wavelength of an electromagnetic wave.

Quite naturally, a question arises. What is the original wavelength of an electromagnetic wave? How do we understand what the original wavelength of an electromagnetic wave we measure?

This is not hard to understand for most situations. At which wavelength each element emits light is known. To illustrate, when an electrical current goes through a glass tube with Hydrogen gas in it in low pressure, Hydrogen atom emits light at the wavelengths given in the table below. We can say that these values are factory settings of the nature for Hydrogen atom.

Wavelength (nm)	Color
656.2	Red
486.1	Blue-green
434.0	Blue-violet
410.1	Violet

On the other hand, if the source and the target reference systems are motionless relative to each other, it is possible to find the original wavelength of the signal since the wavelength doesn’t change. In this case, the wavelength measured at the target is the original wavelength of the signal. 

But now another question arises. How come a signal transmitter with a factory setting of λ₀ can transmit at different wavelengths?

- Hello. Hellooo.
- Yes, sir.
- I’d like to speak to the production manager, please. 
- You are talking to him. How may I help you? My secretary just informed me; I guess you have a complaint. 
- We purchased a laser device radiating in red at 656.2 nanometers. We set up the device and ran it the other day. Bro, this device radiates in all colors almost except red. How come? It radiates in red, blue, violet, ultraviolet; whatever color you like. Are you kidding me?
- I… I don’t understand. Our laser devices are very sensitive. They radiate in only one color and at a certain wavelength. 
- This is just like a disco ball! Sensitive device, huh? Is that what you call it? You can have it back.
- Sir, there must be a manufacturing defect. I’m sending my engineers ASAP. You can rest assured that we’ll replace it if necessary. 
Another question here is this: Could the man who complains about the device be able to recognize that device whose factory setting is 656.2 nanometers can radiate at different wavelengths? I will not answer this question right away.

The topic of wavelength change will appear again and again in the following chapters. I will just put it aside for now.