Working with the Doppler Shift Formula
Topic/Concept: Doppler Shift
Type of Activity: Calculation/Thought Experiment
Prerequisite knowledge required: Need to know the relationship between wavelength, frequency, and velocity for EM waves (see the EM wave tutorial).
Resources required: Writing instruments, paper
Learning Objectives: Better understanding of the Doppler Shift formula.
Common misconceptions:
Detailed description of activity:
I got them to derive the equation: (change in wavelength)/wavelength = (velocity of object)/c. Imagine an object moving at 100 m/s toward you emitting light with wavelength=1 m. I drew a picture of the object as it emitted one full wave of light. I made sure to show how the object had moved some distance by the time it finished emitting the full wave. By drawing the picture, students can see that the light wave appears shorter to a stationary observer. I then asked them the following questions in succession, making sure the whole group was comfortable with the result before going on: How long it took to emit on full wave of light? How far did the object go in this time? How long is the wavelength to the stationary observer?
I then made them do the whole thing again using variables instead of hard numbers. The final result is delta lambda/lambda=v/c. After everyone reached this point, I grilled them about how changing v would affect delta lambda and whatever other relations came to mind. I made a point about emphasizing the physical basis for this change. I said at least 3 or 4 times that the whole origin of the change in wavelength is the fact that the object moves an appreciable distance in the time it emits one full wave of light.
Assessment: You could create a worksheet with this activity on it and grade the worksheet.
Associated files and images: None.
Comments: None.
By Christer Watson (8/99)