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Introductory Electromagnetism

Problems Laboratory

1

Speed Gun

Goals: Apply Doppler shift formula to

moving sources and destinations. Combine

multiple formulas into a new formula.

Identify components of vectors used in

problems.

PROBLEM The radar speed gun is used for many activites that need to find the speed of a moving

object. This can range from tracking the speed of a served tennis ball to identifying cars

that may be violating a speed limit. (U.S. Army photo by Master Sgt. Lek Mateo)

A speed gun aimed at a target moving around a corner may get a different reading than

one moving directly away. You are familiar with a stretch of highway where the road

curves, and cars will change direction by 20o without changing speed. The problem to

consider is how much the speed guns reading varies depending on the speed of the user

and any relative angle in the motion of the target.

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2 Speed Gun

PROBLEM SKILLS When electromagnetic waves are emitted from a moving source at a velocity v relative

to an observer will detect a change in frequencyfof those waves. The speed of light is

constant to all observers, c = 2.998 x 108 m/s, so the observed velocity of those waves

does not change. If the source frequency isfs then the observed frequencyfo is:

(EQ 1)

For speeds that are much less than the speed of light this can be approximated using

(EQ 2)

forx

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Speed Gun 3

3. Apply EQ 1 to the frequency at the car and again from the car back to the gun to

form an expression for the frequency of the reflected wave at the gun in terms of the

orginal frequency and relative velocity.

4. Use the expression from step 3 to write an expression for the change in frequency

divided by the original freqency. Simplify the expression if appropriate.

5. Apply EQ 3 to the frequency at the car and again from the car back to the gun to

form an expression for the frequency of the reflected wave at the gun in terms of the

orginal frequency and relative velocity.

6. Apply EQ 2 to the result from step 5 to simplify the expression.

7. Subtract the original frequency from the result of step 6, then divide that by the orig-

inal frequency. Simplify the expression if appropriate.

8. Calculate the difference between the result from step 4 and step 7 using the vaule

determined in step 2.

9. Share your results with the other groups and discuss any differences between the

groups.

Part B. Moving Cars

10. Use the result of step 7 (corrected as needed after step 9) to detemine the fractional

frequency shift for a car movng with a relative velocity at the speed limit and one at

an excessive speed as suggested in the background information.

11. Find the component of the relative velocity for a car that has gone through the curve

described by the problem compared to a car that has not gone through the curve.

12. Find the ratio of the excessive speed in the background information compared to the

excessive speed from step 11.

13. Repeat step 10 for a car moving at the excessive speed after moving through the

curve using the relative velocity from step 11.

14. Assume the cruiser with the speed gun is moving at the posted speed limit and theother car is moving in a straight stretch of road. Find the relative velocity and use the

expression from step 10 to determine the fractional frequency shift.

15. Repeat step 14, but assume that the target vehicle has passed through the curve.

16. Share your results of part B with the other groups and discuss any differences

between the groups.

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