Answer:
The frequency of the siren in the police car is 1270.45 Hz
Explanation:
Here we have
[tex]f_d = f\frac{v-v_r}{v-v_s}[/tex]
[tex]f = f_d\frac{v-v_s}{v-v_r} = 1310\frac{v-44.2}{v-35}[/tex]
f(v-35) = 1310(v-44.2)
fv -35f = 1310v - 57902....(1)
Also
[tex]f_d = f\frac{v+v_r}{v+v_s}[/tex]
[tex]f = f_d\frac{v+v_s}{v+v_r}[/tex]
[tex]f = f_d\frac{v+44.2}{v+35}[/tex]
f(v + 35) = 1240(v + 44.2)
fv + 35f = 1240v + 54808.....(2)
Subtracting (1) from (2) gives
70f = 112710 -70v
Therefore f = 1610.143 -v
Substituting the value of f in (1) we get
(1610.143 -v)v -35(1610.143 -v) = 1310·v - 57902
Which gives
v²-335.143·v-1546 =0
Factorizing gives
(v + 4.554)(v - 339.697) =0
Therefore, since v is the velocity of sound, we have v = 339.697 m/s
Since our f = 1610.143 -v
f = 1610.143 -339.697 = 1270.45 Hz
