A police radar device bounces radio waves of wavelength 3 mm from the front of a speeding car and measures the Doppler shift in wavelength of the reflected waves. What will be the wavelength shift if the car is moving at 60 mph (80 km/h or 22.2 m/s) (in a 30 mph zone)? Note that the shift is doubled because of the reflection.
A) 0.44 nm
B) 0.44 $\mu$m
C) 4.4 $\mu$m
D) 4.4 m

Question

Quizplus · Accepted Answer

The Doppler shift in wavelength can be calculated using the formula $\Delta \lambda = \frac{v}{c} \lambda$, where $v$ is the speed of the car, $c$ is the speed of light, and $\lambda$ is the original wavelength. Given that the speed of light $c \approx 3 \times 10^8$ m/s, the speed of the car $v = 22.2$ m/s, and the original wavelength $\lambda = 3$ mm = $3 \times 10^{-3}$ m, the shift $\Delta \lambda$ is calculated as follows:$$\Delta \lambda = \frac{v}{c} \lambda = \frac{22.2}{3 \times 10^8} \times 3 \times 10^{-3} = 2.22 \times 10^{-7} \text{ m}$$Since the shift is doubled due to reflection, the total shift is $2 \times 2.22 \times 10^{-7} = 4.44 \times 10^{-7}$ m, which is equal to 0.44 nm.

A Police Radar Device Bounces Radio Waves of Wavelength 3 μ\muμ

A Police Radar Device Bounces Radio Waves of Wavelength 3 $\mu$