Answer
(a) $553.9Hz$ and $455.6Hz$
(b) $y=Asin(3480 t)$ and $y=Asin(2683 t)$
Work Step by Step
Identify the given quantities as $v=110ft/s, v_0=1130ft/s, f_0=500Hz$
(a) Use the formula given, we have $f_1=500(\frac{1130}{1130-110})=553.9Hz$ when the car approaches her, and $f_2=500(\frac{1130}{1130+110})=455.6Hz$ when the car moves away from her.
(b) With the given model of $y=Asin(\omega t)$ where $\omega=2\pi f$, we have $\omega_1=2\pi f_1\approx3480$ and $\omega_2=2\pi f_2\approx2863$ and the model equations are:
$y=Asin(3480 t)$ when the car approaches her, and $y=Asin(2683 t)$ when the car moves away from her.
