   Chapter 28, Problem 31PE

Chapter
Section
Textbook Problem

A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.

To determine

The velocity of the vehicle.

Explanation

Given info:

• The frequency of outgoing radar is 100GHz.
• Convert giga-hertz into hertz.

100GHz=100GHz×109Hz1GHz=1011Hz

• The frequency of the returning echo is 15kHz.
• Convert kilo-hertz into hertz.

15kHz=15kHz×103Hz1kHz=15000Hz

Formula used:

The frequency observed by the car is,

foc=fs1+uc1uc

Frequency observed by the detector,

f0=foc1+uc1ucf0=fs1+uc1uc1+uc1uc=fs(1+uc1uc)     Equation-1

Frequency of the echo,

Δf=fofsΔf=fs(

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