Question

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 10^9 Hz and the speed limit is 65 mi/hr. What is the difference in frequency of the emitted and returned radar wave? (A positive answer means the returned wave has a greater frequency than the emitted wave; a negative answer means the returned wave has a smaller frequency than the emitted wave.)

Answer 1

`\Delta f =1549.86Hz`

Step-by-step explanation:

The Doppler effect is used in some types of radar, to measure the speed of the detected objects. Because the doppler shift affects the wave incident upon the target as well as the wave reflected back to the radar, the change in frequency observed by a radar due to a target moving at relative velocity Δv is twice that from the same target emitting a wave:

`\Delta f = (2\Delta v)/(c) f_0`

Where,

`\Delta v`=is the speed of the receiver with respect to the source: it is positive when the source and the receiver approach.

`f_0`= The emitted frequency

c= speed of light = 3*10^8m/s

Substituting,

`\Delta f = (2\Delta v)/(c) f_0`

`\Delta f = (2(29.06))/(3*10^8)(8*10^9)`

`\Delta f =1549.86Hz`