Math in the News: 6/6/11
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Math in the News: 6/6/11

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In our latest issue of Math in the News we investigate Doppler Radar, and the mathematical equations underlying its use.

In our latest issue of Math in the News we investigate Doppler Radar, and the mathematical equations underlying its use.

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Math in the News: 6/6/11 Math in the News: 6/6/11 Presentation Transcript

  • 6/6/11
  • Doppler Radar
    The Doppler Effect
    Doppler Radar relies on the Doppler Effect, a familiar phenomenon that you experience whenever you hear an ambulance’s siren going past you.
    This diagram shows the sound wave generated from a stationary ambulance.
    The frequency of sound is the ratio of the speed of the sound wave to its wavelength.
  • Doppler Radar
    The Doppler Effect
    But the situation changes when the ambulance starts to move. Seen from above the sound wave is compressed when the ambulance approaches. The sound wave expands when the ambulance moves away from you.
    For a brief video on the Doppler Effect, click here.
  • Doppler Radar
    The Doppler Effect
    As the ambulance approaches, the compressed wavelength creates a higher frequency, based on the speed of the ambulance.
  • Doppler Radar
    The Doppler Effect
    As the ambulance moves away, the expanded wavelength creates a lower frequency, also based on the speed of the ambulance.
  • Doppler Radar
    The Doppler Effect
    The same effect applies with police radar guns that measure a moving car’s speed.
    The radar gun sends out a radio wave signal that will bounce off the moving car.
  • Doppler Radar
    The Doppler Effect
    As the radio wave bounces off the car, the reflected wave shows either a higher or lower frequency, depending on the what direction the car is moving relative to the radar gun.
    The radar gun measures the reflected wave’s frequency to determine the speed of the car.
  • Doppler Radar
    The Doppler Effect
    The same idea applies to weather radar. A radio wave is aimed at an oncoming storm.
    The wave bounces off the storm front and is measured by the weather radar.
  • Doppler Radar
    The Doppler Effect
    The reflected radio wave from a storm front moving toward the weather radar has a higher frequency.
    The reflected radio wave from a storm front moving away from the weather radar has a lower frequency.
  • Doppler Radar
    The Doppler Effect
    The color coding you see on Doppler radar maps has to do with the frequency of the reflected radio signal, and also with the amount of rainfall.
    The blue end of the spectrum is for light rain, while the red end is for more intense precipitation.
  • Doppler Radar
    The Doppler Effect
    The Doppler shift formula for radio waves is different from sound waves. The formula is shown here.
    The two measures for frequency are based on the original radio wave sent from the weather radar (fs) and the measured frequency reflected by the storm (fo).
  • Doppler Radar
    The Doppler Effect
    Since the point of Doppler Radar is to measure the speed and direction of the storm, then we need to rewrite the formula to solve for v, the speed of the storm.
    The solution is shown here.
  • Doppler Radar
    The Doppler Effect
    You can convert from km/hr to miles per hour.
    This formula can then be used to determine the speed and direction of a storm.
  • Doppler Radar
    The Doppler Effect
    Set up a spreadsheet like the one shown. For fs use a 1 GHz frequency (1 billion Hertz).
    Inputting the data in the cells show, input the formula shown in B6.
    Input different values for fo to simulate different speeds and directions for storms.
    Let v > 0 be for approaching storms, and v < 0 for receding storms.