A galaxy in the constellation Ursa Major is receding from Earth at 15,000 km/s. If one of the characteristic wavelengths of the light which the galaxy emits is 550 nm, what is the corresponding wavelength measured by astronomers on Earth? Also, calculate the red shift parameter z of this galaxy.

A sinusoidal plane electromagnetic wave of frequency 20 GHz moves in the positive y direction and its electric field is directed along the z-axis. The amplitude of the electric field is 10 V/m. The start of time is chosen so that at t = 0, the electric field has a value +(10 V/m)k at the origin. a. Write the function that describes the electric field of the wave as a function of position y and time t. Hint: Among other things, you need to decide whether to use a cosine or sine function, and whether a negative sign is needed inside and/or outside the sine/cosine function. b. Explain why the electric field is not a function of the x or z coordinate. c. Find the function that describes magnetic field of the wave as a function of position y and time t.

c

Two starships, the Enterprise and the Constitution, are approaching each other head-on from a great distance. The separation between them is decreasing at a rate of 812.5 km/skm/s. The Enterprise sends a laser signal toward the Constitution. If the Constitution observes a wavelength λ=675.3nm, what wavelength was emitted by the Enterprise? Express your answer to four significant figures and include appropriate units.