I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Wednesday, August 13, 2008

Should you Brake, Slow Down or Go?

How fast would you need to be traveling towards a red traffic light to see it appear as green?

You're a little rusty on physics, and then you pull this question out?? Well, you asked for it...

The wavelength of green light is around 530 nm, yielding a frequency of 5.66*10^14 Hz (566 THz). Red light has an average wavelength of 685 nm, with a frequency of 438 THz. According to my graduate E&M book, the relativistic Doppler shift (different from the classical Doppler shift, since light travels the same speed in all inertial reference frames) is given by:

w' = gamma * w * (1-Beta*cos(theta))

w' = new frequency w = old frequency gamma = 1 / sqrt(1-Beta^2) Beta = v/c v = your velocity c = velocity of light theta = angle between your velocity vector and that of the light (0 degrees in this case, assuming you're headed straight at the traffic light)

Plugging everything in:

566 = 438/sqrt(1-Beta^2)*(1-Beta)

and solving, yields:

Beta = -0.25

Therefore, you need to go 1/4 the speed of light, and the negative means you need to go the opposite direction of the light.

So you must go 1/4 the speed of light (about 75,000,000 m/s, or about 671,000,000 mph) toward the traffic light. I know my car can't go that fast ;-)

Abe - I love reading your answers to these questions. Between you and Mike I am learning something everyday that I wouldn't have the opportunity to learn in my normal day to day. Thanks guys! Serena

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You're a little rusty on physics, and then you pull this question out?? Well, you asked for it...

ReplyDeleteThe wavelength of green light is around 530 nm, yielding a frequency of 5.66*10^14 Hz (566 THz). Red light has an average wavelength of 685 nm, with a frequency of 438 THz. According to my graduate E&M book, the relativistic Doppler shift (different from the classical Doppler shift, since light travels the same speed in all inertial reference frames) is given by:

w' = gamma * w * (1-Beta*cos(theta))

w' = new frequency

w = old frequency

gamma = 1 / sqrt(1-Beta^2)

Beta = v/c

v = your velocity

c = velocity of light

theta = angle between your velocity vector and that of the light (0 degrees in this case, assuming you're headed straight at the traffic light)

Plugging everything in:

566 = 438/sqrt(1-Beta^2)*(1-Beta)

and solving, yields:

Beta = -0.25

Therefore, you need to go 1/4 the speed of light, and the negative means you need to go the opposite direction of the light.

So you must go 1/4 the speed of light (about 75,000,000 m/s, or about 671,000,000 mph) toward the traffic light. I know my car can't go that fast ;-)

Abe -

ReplyDeleteI love reading your answers to these questions. Between you and Mike I am learning something everyday that I wouldn't have the opportunity to learn in my normal day to day.

Thanks guys!

Serena

As always abe, your answer is so much better than I could have said it.

ReplyDeleteThanks!

I would just wait until it turns green ;)

ReplyDeleteJust watch out for those cameras!

ReplyDelete