On a hot $91\mathrm{.}4$F $(306$ K$)$ day at a racetrack, a Formula One racecar is traveling at a speed of $1\mathrm{.}55102$ mph $(69\mathrm{.}3$ m$/$s$)$ away from a stationary siren emitting sound waves at a frequency of $3\mathrm{.}65102$ Hz$.$

$($a$)$ Determine the sound speed for the given temperature. $($Enter your answer to at least $1$ decimal place.$)$

m$/$s

$($b$)$ What frequency did the racecar driver hear?

Hz