Question $2(15$ marks$)$

Suppose an ambulance moving at $15\frac{m}{s}$ to the right, emits siren of sound frequency $f=700$ Hz while a truck is moving to the left with speed of $38\frac{m}{s}$ and approaching the ambulance. Given sound speed in air $=343\frac{m}{s}.$

$($a$)$ Find the frequency $f_1$ that the truck's driver would hear.

$(5$ marks$)$

$($b$)$ What frequency $f_2$ is detected by the ambulance in the signal reflected back to it by the truck?

$(5$ marks$)$

$($c$)$ If the truck passed and moving away from the ambulance, find the frequency $f_3$ that the truck's driver would hear.

$(5$ marks$)$