A $4\mathrm{.}5-$Hz wave with an amplitude of $12$ cm and a wavelength of $27$ cm travels along a rope.

a$)$ How far does a given peak on the wave travel in an interval of $0\mathrm{.}50$ s$?$

b$)$ A part of the rope is marked with a dot of red paint. What is the distance through which this dot travels in $0\mathrm{.}50$ s$?$