Chapter 28, Problem 31PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
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 100â€‰GHz.
• Convert giga-hertz into hertz.

â€ƒâ€ƒ100â€‰GHzâ€‰=â€‰100â€‰GHzÃ—109Hz1â€‰GHz=â€‰1011â€‰Hz

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

â€ƒâ€ƒ15â€‰kHzâ€‰=â€‰15â€‰kHzÃ—103Hz1â€‰kHz=â€‰15000â€‰Hz

Formula used:

The frequency observed by the car is,

â€ƒâ€ƒfocâ€‰=â€‰fsâ€‰1+uc1âˆ’uc

Frequency observed by the detector,

â€ƒâ€ƒf0â€‰=â€‰focâ€‰1+uc1âˆ’ucf0â€‰=fsâ€‰1+uc1âˆ’uc1+uc1âˆ’uc=â€‰fs(1+uc1âˆ’uc) â€ƒâ€ƒâ€ƒâ€ƒEquation-1

Frequency of the echo,

â€ƒâ€ƒÎ”f=foâ€‰âˆ’â€‰fsÎ”f=â€‰fs(

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