A police radar bounces microwaves of wavelength 3 mm from the front of a speeding car and measures the Doppler shift in wavelength of the reflected waves. The shift is doubled because of the reflection. What will be the wavelength shift if the speeding car is moving at 60 mph (80 km/h or 22.2 ms^-1)?

Question

Quizplus · Accepted Answer

The Doppler shift in wavelength is given by:$$\Delta \lambda = \frac{\lambda}{c} v$$where:* $\Delta \lambda$ is the change in wavelength* $\lambda$ is the original wavelength* $c$ is the speed of light* $v$ is the speed of the objectIn this case, the original wavelength is 3 mm, the speed of light is 3 x 10^8 m/s, and the speed of the car is 22.2 m/s. Plugging these values into the equation, we get:$$\Delta \lambda = \frac{3 \times 10^{-3} \text{ m}}{3 \times 10^8 \text{ m/s}} \times 22.2 \text{ m/s} = 0.44 \times 10^{-9} \text{ m} = 0.44 \text{ nm}$$Since the shift is doubled because of the reflection, the total shift is 0.88 nm.

A Police Radar Bounces Microwaves of Wavelength 3 Mm from the Front