Red light Doppler shift

I was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler shift that made the light look green to me; after all, I was approaching it. So he waived the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?

Originally posted by Jirakon
I was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler ...[text shortened]... d the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?

Ok, it appeared 520nm, or 0.00000052m
Speed of light = 299792458
V=Flamda
299792458=0.00000052F
F=576523957692308 Hz

Now it was actually 650nm, or 0.00000065m
So V = 576523957692308 x 0.00000065
Where V is the speed of light, plus the speed of your car.
V = 374740572.5
374740572.5 - speed of light = 74 948 114.5

So you were travelling at 74948114.5meters/second
= 208189.207meters/hour
= 129.362776mph

so you were travelling at 129mph.

Great question.

Originally posted by Jirakon
I was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler ...[text shortened]... d the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?

Too fast wayyyyy too fast..... Haven't done one of these since school....
using W as wavelength since I don't have a lambda and /\ since I don't have delta

f' = f + f(v)/c

f = c/W

c/W' = c/W + (cv/w)/c

W'= W + v/Wc

/\W (c) = v (W) i think, could be wrong.....

/\W(c)/W = v


1.2X10^-7(3X10^8)/6.5X10^-7 = v (All in Meters per second)

V = 1.24 X 10^8 MPH


Too fast........

Please correct if this is wrong.... As I said its been a long time since physics at uni and this is all from memory....

Originally posted by doodinthemood
Ok, it appeared 520nm, or 0.00000052m
Speed of light = 299792458
V=Flamda
299792458=0.00000052F
F=576523957692308 Hz

Now it was actually 650nm, or 0.00000065m
So V = 576523957692308 x 0.00000065
Where V is the speed of light, plus the speed of your car.
V = 374740572.5
374740572.5 - speed of light = 74 948 114.5

So you were travelling at ...[text shortened]... = 208189.207meters/hour
= 129.362776mph

so you were travelling at 129mph.

Great question.

Dammnit you got there first but....

Has to be faster surely? I've done 129 mph and not see a green light where once there was a red one?

Well I haven't but you get the point.....

Originally posted by doodinthemood
Ok, it appeared 520nm, or 0.00000052m
Speed of light = 299792458
V=Flamda
299792458=0.00000052F
F=576523957692308 Hz

Now it was actually 650nm, or 0.00000065m
So V = 576523957692308 x 0.00000065
Where V is the speed of light, plus the speed of your car.
V = 374740572.5
374740572.5 - speed of light = 74 948 114.5

So you were travelling at ...[text shortened]... = 208189.207meters/hour
= 129.362776mph

so you were travelling at 129mph.

Great question.

i think you did something wrong with the dimensional analysis... 1 meter/sec is appx 2.2 mph

so in very rough numbers it should be more than double the number of meters/second - i.e. 1.5 x 10^8 miles per hour... using google to convert, it gave me 167654157 mph which is about right

i think in going from seconds to hours you divided by 3600 where you should have multiplied - this gets it back to the correct magnitude of answers 🙂 and damn i wish i could drive that fast.

Originally posted by Mexico
Dammnit you got there first but....

Has to be faster surely? I've done 129 mph and not see a green light where once there was a red one?

Well I haven't but you get the point.....

129 mph on a road with traffic lights?

You should lose your drivers license, if you have any.

Originally posted by doodinthemood
... so you were travelling at 129mph.

Great question.

129 mph is not very fast. In germany they don't have any speed limits on some parts of the Autobahn. When I was there, pressing the pedal, I didn't see any color shifts anywhere, the trees weren't blue, the sun stayed yellow.

I think we should be talking about way far higher speeds here...

Originally posted by Jirakon
I was driving down the street on an uneventful morning, and I drove past an ordinary traffic light that appeared green to me (wavelength 530nm). Suddenly a policeman came behind me, pulled me over, and told me I ran a red light (wavelength 650nm). I assured him that I saw a green light, but he was convinced it was red. I told him it must have been a Doppler ...[text shortened]... d the red light charge, but gave me a ticket for a different reason. How fast was I going (mph)?

haha... that's the best excuse I have ever seen 😀
but you would have to be going REALLY fast to see a doppler shift of around 20%.
Galaxies with that amount of redshift have to be moving at relativistic speeds.

Use the relativistic formula; you'll need it. Let {x} = the square root of x.

f(observed) = f(source) {(1 + v/c)/(1 - v/c)} for approaching objects.

Yea I thought it couldn't be that low..... Can someone tell me if I was right..... I think it is but as I said its from memory so maybe not......

Originally posted by Mexico
Yea I thought it couldn't be that low..... Can someone tell me if I was right..... I think it is but as I said its from memory so maybe not......

"classicaly" the velocity (in units of c) of the wave should be v = (1 - 530/650) = 0.1846
relativistically we use the equation given by Jirakon in the previous post, and gives v=0.2013

In this velocity range, the relativistic effect exists , but it's not that significant.

To find the "classical" Doppler Shift, imagine an indian on a horse, throwing arrows at you every few seconds, let's say 1 arrow per second (this is the frequency).
If the indian starts moving towards you, he'll keep firing 1 arrow per second, but you'll be shot more frequently.
The analogy with sound or other wave is evident. The wavelength of a wave would correspond to the distance between consecutive shots.
Let's calculate it.
We only need to know the speed of the arrow (v).
The distance that first arrow moved from the point it was fired until the second arrow is fired is v * t (t is time between shots, equal to 1/f )
But in this time, the indian moved a little too! How much? Simply v_indian * t ... easy!
So the distance between arrows is simply v * t - v_indian*t
In wave language, lambda_observed=(v_wave - v_source) * t
Now, t, is equal to lambda / v_wave.
So, lambda_observed = lambda * (v_wave - v_source) / v_wave
If you want frequencies, know that lambda = v_wave / f

For this problem , we have wavelenghts and v_wave = 1 (in units of c)
so,
lambda_observed / lambda = (1 - v_source)
v_source = 1 - lambda_observed / lambda

In this velocity range, the relativistic effect exists , but it's not that significant.

Not significant? 124 million mph to 135 million mph? I would call an eight percent error pretty significant.

The answer is ~135 million mph.

I have a confession to make. This story is not true. (glad I got that off my chest)

Originally posted by Jirakon
In this velocity range, the relativistic effect exists , but it's not that significant.

Not significant? 124 million mph to 135 million mph? I would call an eight percent error pretty significant.

The answer is ~135 million mph.

I have a confession to make. This story is not true. (glad I got that off my chest)

Well... for a speed limit of 80 mph (?) - who the hell uses mph... - it's quite irrelevant 🙂
And the idea of the problem is to show that you would have to move at a speed comparable to the speed of the wave to see a wave change.

Originally posted by Jirakon
In this velocity range, the relativistic effect exists , but it's not that significant.

Not significant? 124 million mph to 135 million mph? I would call an eight percent error pretty significant.

The answer is ~135 million mph.

I have a confession to make. This story is not true. (glad I got that off my chest)

If he was going that fast, he wouldn't have had TIME to get a ticket, 167 million mph is what, about 0.16C or so? In one second he would have been 30,000 miles away and trying to figure out how to get home🙂