plab2
TRANSCRIPT
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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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