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A police car on the side of the road (at rest) uses a radar gun to catch speeders as they approach it. The frequency the radar gun emits is 8 x 109 Hz and the speed limit is 65 mi/hr. What is the difference in frequency of the emitted and returned radar wave

Respuesta :

Answer:

[tex]\Delta f = 1.49 \times 10^9 Hz[/tex]

Explanation:

Apparent frequency that is received to the speeder is given as

[tex]f_1 = f_0\frac{v + v_o}{v}[/tex]

[tex]f_1 = (8 \times 10^9)\frac{340 + v_o}{340}[/tex]

here we know that

[tex]v_o = 65 mph = 29 m/s[/tex]

now we have

[tex]f_1 = (8 \times 10^9)\frac{340 + 29}{340}[/tex]

[tex]f_1 = 8.68 \times 10^9 Hz[/tex]

now the frequency that is received back from the speeder is given as

[tex]f_2 = f_1\frac{v}{v- v_o}[/tex]

[tex]f_2 = (8.68 \times 10^9}\frac{340}{340 - 29}[/tex]

[tex]f_2 = 9.49 \times 10^9 Hz[/tex]

So difference is the frequency is given as

[tex]\Delta f = 9.49 \times 10^9 - 8 \times 10^9[/tex]

[tex]\Delta f = 1.49 \times 10^9 Hz[/tex]

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