A $6\mathrm{.}0-$m wire with a mass of $50$ g$,$ is under tension. A transverse wave, for which the

frequency is $810$ Hz$,$ the wavelength is $0\mathrm{.}40$ m$,$ and the amplitude is $4\mathrm{.}0$ mm$,$ is

propagating on the wire. How long does it take for a crest of this wave to travel the

length of the wire?

$18.$ A factory siren indicating the end of a shift has a frequency of $90\mathrm{.}0$ Hz$.$ The speed of

sound is $343$ m$/$s$.$

$($a$)$ What frequency is perceived by the occupant of a car traveling towards the factory at

$25\mathrm{.}0$ m$/$s$?$

$($b$)$ What frequency is perceived by the occupant of a car traveling away from the factory

at $30\mathrm{.}0$ m$/$s$?$