Answer:
Explanation:
In the first case you can use the expression for the Doppler effect when the source is getting closer and getting away
[tex]f'=f(\frac{v}{v-v_{s}})[/tex] ( 1 )
[tex]f''=f(\frac{v}{v+v_s})[/tex] ( 2 )
f' = perceived frequency when the source is getting closer
f'' = perceived frequency when the source is getting away
f = source frequency
v = relative speed
vs = sound speed
by dividing (1) and (2) you have
[tex]\frac{f'}{f''}=\frac{f}{f}\frac{\frac{v}{v-v_s}}{\frac{v}{v+v_s}}=\frac{v+v_s}{v-v_s}\\\\f'v-f'v_s=f''v+f''v_s\\\\v(f'-f'')=v_s(f''+f')\\\\v=v_s\frac{f''+f'}{f'-f''}=(340\frac{m}{s})\frac{1370Hz+1330Hz}{1370Hz-1330Hz}=67.5\frac{m}{s}[/tex]
but this is the relative velocity, you have that
[tex]v=v_{sir}-v_{car}\\v_{sir}=v+v_{car}=67.5\frac{m}{s}+35\frac{m}{s}=102.5\frac{m}{s}[/tex]
a. hence, the speed of the police car is 102.5m/s
