Question

Police radar detects the speed of a car (Fig. P24.13) as follows. Microwaves of a precisely known frequency are broadcast toward the car. The moving car reflects the microwaves with a Doppler shift. The reflected waves are received and combined with an attenuated version of the transmitted wave. Beats occur between the two microwave signals. The beat frequency is measured. (a) For an electromagnetic wave reflected back to its source from a mirror approaching at speed $v$, show that the reflected wave has frequency $$f=f_{\text {source }} \frac{c+v}{c-v}$$ where $f_{\text {source }}$ is the source frequency. (b) When $v$ is much less than $c$, the beat frequency is much smaller than the transmitted frequency. In this case, use the approximation $f+f_{\text {source }}=2 f_{\text {source }}$ and show that the beat frequency can be written as $f_{\text {beat }}=2 v / \lambda .$ (c) What beat frequency is measured for a car speed of $30.0 \mathrm{m} / \mathrm{s}$ if the microwaves have frequency $10.0 \mathrm{GHz} ?(\mathrm{d})$ If the beat frequency measurement is accurate to $\pm 5 \mathrm{Hz}$, how accurate is the speed measurement?

          Police radar detects the speed of a car (Fig. P24.13) as follows. Microwaves of a precisely known frequency are broadcast toward the car. The moving car reflects the microwaves with a Doppler shift. The reflected waves are received and combined with an attenuated version of the transmitted wave. Beats occur between the two microwave signals. The beat frequency is measured. (a) For an electromagnetic wave reflected back to its source from a mirror approaching at speed $v$, show that the reflected wave has frequency $$f=f_{\text {source }} \frac{c+v}{c-v}$$ where $f_{\text {source }}$ is the source frequency. (b) When $v$ is much less than $c$, the beat frequency is much smaller than the transmitted frequency. In this case, use the approximation $f+f_{\text {source }}=2 f_{\text {source }}$ and show that the beat frequency can be written as $f_{\text {beat }}=2 v / \lambda .$ (c) What beat frequency is measured for a car speed of $30.0 \mathrm{m} / \mathrm{s}$ if the microwaves have frequency $10.0 \mathrm{GHz} ?(\mathrm{d})$ If the beat frequency measurement is accurate to $\pm 5 \mathrm{Hz}$, how accurate is the speed measurement?

Added by Bill R.

Question

Please give Ace some feedback