Answer:
The frequency of the siren in the police car is f=1277.6 Hz.
Explanation:
The frequency percibed by a receptor wich is in movement with an emisor moving too, is given by
[tex]f^{'}=f\frac{v+v_{r}}{v-v_{f}}[/tex] if the emisor is approaching and
[tex]f^{''}=f\frac{v-v_{r}}{v+v_{f}}[/tex] if the emisor is moving away from the receptor.
Where [tex]f^{'}[/tex] is the frequency when approaching, [tex]f^{''}[/tex] the frequency when moving away, [tex]v[/tex] is the speed of sound, [tex]v_{r}[/tex] is the velocity of the receiver, and [tex]v_{f}[/tex] is the velocity of the emisor (wich we don't know in advance). From the second equation we clear [tex]v_{f}[/tex] and put it in the first equation, obtaining
[tex]f=\frac{1310*2*343}{343+35}*\frac{1}{1+\frac{1310}{1240}*\frac{343-35}{343+35}}[/tex]
thus
[tex]f=1277.6 Hz[/tex]
is the frequency of the siren in the police car.
