On a hot $91\mathrm{.}4F(306K)$ day at a racetrack, a Formula One racecar is traveling at a speed of $1\mathrm{.}80{10}^{2}mph(80\mathrm{.}5\frac{m}{s})$ away from a stationary siren emitting sound waves at a frequency of $3\mathrm{.}75{10}^{2}Hz.$

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

$351\frac{m}{s}$

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

Your response is within $10\%$ of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four$-$digit accuracy to minimize roundoff error. Hz