Activity: Doppler

Aims

  • Introduce the Doppler effect.
  • Use a GeoGebra simulation to show how the Doppler equation is derived.
  • Measure the change in frequency using a ripple tank simulation.

Introduction

The Doppler effect is the change in frequency due to relative motion between source and observer (HL p181). This is often observed when a car drives past sounding it's horn (not such a regular occurrence where I live).

The frequency is increased when the car approaches because the car catches up with the waves causing them to be squashed. The result is a reduction in wavelength leading to a higher frequency (f = c/λ). This can be seen on the simulation below.


Try adjusting the velocity of the source and waves, you can also change the frequency.

Set the values to

v = 2 ms-1
c = 3 ms-1
fo = 1 Hz

Advance the time to 6s.

Without revealing the answers calculate:

  1. The number of cycles of the wave produced in 6s.
  2. The distance travelled by the wave in 6s
  3. The distance travelled by the source in 6s
  4. The distance between the source and the furthest wavefront to the right.
  5. The wavelength of the wave to the right.
  6. The frequency observed to an observer to the right of the source

Reveal the values to check you have the right answer.

So the wavelength is lambda equals fraction numerator c t minus v t over denominator f subscript o t end fraction equals fraction numerator c minus v over denominator f subscript o end fraction

The observed frequency is f apostrophe equals c over lambda equals fraction numerator c f subscript o over denominator c minus v end fraction Check this out by using this equation to solve the previous problem.

Repeat the process for the waves to the left of the source.

Measuring the Doppler Effect

Now you are going to measure the Doppler Effect for waves in a simulated ripple tank using video analysis.

  • Download the video from here.
  • Open LoggerPro and insert the video (insert > movie).
  • Determine the frequency of the source by measuring the time for the formation of 10 waves. This can be done by using the frame time displayed on the video window.
  • Determine the frequency ahead of the source by measuring the time for 10 waves to pass the bottom of the window.
  • Using the “set scale” tool set the width of the video window to 1m.
  • Use the video analysis tools to measure the velocity of the source and waves from the gradient of displacement time graphs. (you can do both on one graph)
  • Use the Doppler equation to calculate the change in frequency. Is it consistent with your other results?

My values

fo = 5.4 Hz
f’ = 7.5 Hz

v = 0.089 ms-1
c = 0.37 ms-1

Determining the velocity of a car

Use Audacity to determine the frequency of the car in the video above as it approaches and recedes and passes the observer. Use these values to find the velocity of the car. Use the average as the source frequency.

  • Estimate the cars velocity from its motion.
  • Does your Doppler shift value match your expectations?

Moving observer

Doppler shift is also experienced when an observer moves towards or away from a source that is stationary relative to the medium. This effect is simply due to the relative velocity between the observer and source.

Interesting observation

Standing on a bridge over a river I noticed that waves were being formed by water dripping from the bridge. This was before the days of mobile phones with video cameras so I didn’t video it but this is what it looked like.

  • An observer at A (stationary relative to the bridge) measures the wave frequency, is it higher, lower or the same as the frequency of the drips falling off the bridge?

Ending on a bang

Several actually.

Notice the cone behind the plane on some of these clips, try to reproduce this in the GeoGebra simulation.

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