# Object blueshifted

1. Jul 4, 2009

### keepitmoving

i must be missing something here. If an object is moving toward another object and emitting a light at a certain frequency, it becomes blueshifted. If the light has a certain initial frequency and must maintain a speed of c, it therefore must cover a certain distance (c x time) with greater than the initail frequency (blueshifted), so wherre did the additional vibrations come from? In other words since there are a certain number of vibrations required per distance, wjere did the extra vibrations come from to maintain that added frequency times time?

2. Jul 4, 2009

### JesseM

Re: blueshift

There are no additional vibrations, it's just that if the emitter is approaching the observer then this means that each successive peak of the wave is emitted at a shorter distance from the observer than the previous peak was emitted, so if each peak moves towards him at the same speed of c, he'll see them arrive more closely-packed than if the emitter were at rest relative to him.

3. Jul 5, 2009

### Janus

Staff Emeritus
Re: blueshift

For instance, for a source stationary with respect to an observer you get this:

But when the source is moving with respect to the observer you get this:

Note that each wave still travels at a constant speed from the point of emission, each successive wave is emitting closer to the observer to the right, causing each wave to follow more closely behind the other.

4. Jul 5, 2009

### keepitmoving

Re: blueshift

this is whats a problem for me. If a light beam emits say 10 waves per mile and this gets that wave a velocity of say c, then if you crush those waves down to say, 10 waves per half mile, how can that bunch of waves maintain the same speed c? I must be missing something. Thanks for your help.

5. Jul 5, 2009

### JesseM

Re: blueshift

Suppose an emitter is moving towards me at 0.6c, sending out a wave peak once every 20 seconds in its own frame. Since the peaks move at c in its frame, in the emitter's frame the previous peak will be 20 light-seconds away when it emits a new peak, so the distance between successive peaks (the wavelength) is 20 light-seconds in its frame. In my frame the emitter's time is dilated by a factor of $$\frac{1}{\sqrt{1 - 0.6^2}}$$ = 1.25, so in my frame it only emits peaks once every 25 seconds. So, if it emits peak #1 when its at a distance of 100 light-seconds from me, then 25 seconds later when it's emitting peak #2 in my frame, peak #1 was traveling at c so it'll have gotten 25 light-seconds closer to me, meaning it'll only be 75 light-seconds away from me. But in that same time the emitter was approaching me at 0.6c, so it'll have gotten 25*0.6 = 15 light-seconds closer to me, meaning when it emits peak #2 it'll be at a distance of 85 light-seconds away from me. So, at the moment peak #2 is emitted it's 85-75=10 light-seconds further away from me than peak #1, and since both peaks move at c they'll continue to be 10 light-seconds apart as they approach me (the wavelength is 10 light-seconds, shorter than in the emitter's frame), meaning they'll hit me 10 seconds apart even though they were emitted 25 seconds apart in my frame.

Last edited: Jul 5, 2009
6. Jul 5, 2009

### keepitmoving

Re: blueshift

let me ask this please. I saw a movie depiction of blueshift - the emitter emitted and a circle was drawn that represents the first wave going out. The second light wave was emitted from the moving emitter and then the third and fourth etc. Each successive wave was closer to each other than a non moving emitter. In other words in the movie the the waves propagated out but were closer together an not farther out than if they had been emitted by a non moving emitter. Maybe i was seeing a depiction of sound wave though.

7. Jul 5, 2009

### JesseM

Re: blueshift

If the waves are emitted in the same direction the emitter is moving they'll be closer together, yes (and if they're emitted opposite to the direction of motion they'll be farther apart). This is true in my example above--the emitter is moving towards the observer, and the peaks emitted in the direction of the observer are only 10 light-seconds apart, even though in the emitter's own frame they are 20 light-seconds apart.

8. Jul 5, 2009

### keepitmoving

Re: blueshift

thank you. But if the waves are only 10 light seconds apart rather than 20, how can they propagate at full speed? They didnt in the movie anyway. I don`t understand the relevance of the observer other than the observer who is the emitter. There can be many observers, each with a different frame of reference. How does the light pick the one to consider?

9. Jul 5, 2009

### JesseM

Re: blueshift

Why shouldn't they? If you look at my example, it was because they move at c that the first peak was 25 light-seconds closer to the observer 25 seconds after it was emitted 100 light-seconds away from him (i.e. the first peak was emitted 100 light-seconds away from the observer, then 25 seconds later it was 75 light-seconds away), at which point the emitter itself was 15 light-seconds closer to the observer than it was when it emitted the first peak (i.e. 25 seconds after it emitted the first peak it was 85 light-seconds away from the observer), and that was the moment it emitted the second peak, so the distance between the two peaks was 25-15=10. By the way, hopefully you understand that when I use the words "light-second" that's a unit of distance akin to a light year, a light-second is just the distance light travels in one second, i.e. 299792458 meters.
Maybe they were showing sound waves being emitted from the perspective of the frame of an emitter which is moving relative to the air, then (in the emitter's frame waves directed forward do move slower than the speed of sound). But in relativity the peaks move at the same speed of c in all frames.
The light doesn't pick anyone, you can analyze the same light wave from the perspective of different frames. But in the case of the Doppler effect we want to know how often a new peak is passing each observer, so if an observer is at rest relative to the emitter and standing right in front of it he'll see a new peak passing him every 20 seconds as measured by his own clock, then later those same peaks will reach the position of the other observer who the emitter is moving towards, and a new peak will pass that observer every 10 seconds according to his clock.

Last edited: Jul 5, 2009
10. Jul 5, 2009

### keepitmoving

Re: blueshift

i thank you very much for your help.

11. Jul 5, 2009

### keepitmoving

Re: blueshift

it must have been a sound wave movie i was watching. I just caught the end of it and got to thinking.