The initials $$FM$$ stand for frequency modulation. When broadcasting a radio wave, the constant frequency $$B$$ in our problems becomes a varying quantity, f$($t$),$ such that

y $$ Asin$[2$ f $($t$)]$t $.$ This causes the waves to have an inconsistent wavelength. The FCA

assigns each radio station a $$band$-$width$$ around an assigned frequency in megahertz, MHz$,$ which is simply a million waves$/$second$.$ For example, $98\mathrm{.}7$ is allowed to let it$$s frequencies vary slightly above$/$below $98\mathrm{.}7$ MHz$.$

a$.$ Suppose a FM radio station is assigned an equation of

y $$ Asin$[2(93,200,00010,000$sin$500$t$)]$t $.$ What is the assigned frequency in

MHz$?$

$(2)$

Give the minimum and maximum frequencies of the FM radio station over time. $(2)$

If you$$ve ever changed stations while traveling, you may have been able to hear $2$ FM stations at the same time. Explain how this can happen. $(1)$