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Phy 3031 Modern physics, Spring 2007
Homework set #5. Due at the start of class on Monday, February 4, 2007.
For numerical answers give two significant digits. The first should be correct, the second can
be approximate.
1. While driving slowly you see a red (λ = 650 nm) stoplight at the next corner. There
appears to be no cross traffic, so you turn on the turbo chargers and accelerate until
the doppler shift of the red light is enough to make the color look green (λ = 500 nm)
to you as you approach the intersection.
(a) How fast were you going through the intersection?
(b) After passing through the intersection and before slowing down, when you look
in your review mirror what is the wavelength of the light that you see?
2. My twin and I synchronize our watches and he gets on a rocket and flies at a speed
of 0.6c to a planet which is one light-year away as measured in the Earth’s frame of
reference. As soon as he reaches the planet, he turns around and returns at a speed
0.8c.
(a) When my twin returns to the Earth, how much time has elapsed on my watch?
(b) When the twin returns to the Earth, how much time has elapsed on his watch?
3. Event #1 occurs at time t1 = 17 m/c, and x1 = 2 m, y1 = 4 m, z1 = 5 m . Event #2
occurs at time t2 = 12 m/c, and x2 = 5 m, y2 = 5 m, z2 = 5 m.
(a) Is there a frame of reference in which these two events occur at the same time?
(b) Is there a frame of reference in which these two events occur at the same place?
4. A friend of yours travels with a constant speed to Alpha Centauri, which is 4 lightyears away, and then immediately returns at the same speed. He claims that the trip
took just 6 years.
(a) What was his speed while traveling, relative to the Earth?
(b) How long was he away as measured on your watch?