A light source flashes with a frequency of $1\mathrm{.}01015$ Hz$.$ The radiation is reflected by a mirror that

moves at a speed of $100$ km$/$s away from the source. How much does the frequency of the

reflected radiation received at the source differ from the original emitted frequency?

$6\mathrm{.}661011$

Problem $3$: During a deep$-$space survey, a galaxy is observed with a red$-$shift of $0\mathrm{.}450.$ With what speed is the

galaxy moving away from us$?$ The red shift is defined as $$

$0$

$=0$

$0$

$,$ where $0$ is the proper

wavelength in the frame of the source that moves with velocity $$ relative to us$,$ and $$ is the

wavelength we receive.

$0\mathrm{.}355$

Special Theory of Relativity

Problem $1$: A cube of metal with sides of length a sits at rest in frame S with one edge parallel to the x$-$axis. The

cube thus has volume V $=3.$ Frame S$$ moves along the x$-$axis with a speed $.$ As measured by an

observer in frame S$,$ what is the volume of the metal cube?

$=312$

$2$