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The police radar gun emits an electromagnetic wave with a frequency of 8.0 × 10 ⁹ Hz and is pointed at your moving car essentially head-on. When the reflected wave is captured by the gun, its electronics measure the incoming frequency to be 2100 Hz greater than the emitted wave. Presuming the police was parked, how fast were you going?

User CyrilFind
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Final answer:

The police radar gun emits an electromagnetic wave with a frequency of 8.0 × 10^9 Hz and measures a change in frequency of 2100 Hz when the reflected wave is captured. By using the formula for the Doppler effect, we can determine the speed of the car. The car was moving at a speed of approximately 0.79 m/s.

Step-by-step explanation:

The police radar gun uses the Doppler effect to measure the speed of moving vehicles. In this case, the radar gun emits an electromagnetic wave with a frequency of 8.0 × 109 Hz. When the reflected wave is captured, its frequency is measured to be 2100 Hz greater than the emitted wave. By using the formula for the Doppler effect, we can determine the velocity of the vehicle.

First, we need to find the change in frequency:

  • Δf = observed frequency - emitted frequency
  • = 2100 Hz

Next, we can use the formula for the Doppler effect:

  • Δf / f = v / c
  • where:
  • Δf is the change in frequency
  • f is the emitted frequency
  • v is the velocity of the vehicle
  • c is the speed of light

Substituting the given values into the equation:

  • v = (Δf / f) * c
  • = (2100 Hz / 8.0 × 109 Hz) * 3.00 × 108 m/s

Calculating the velocity:

  • v = 0.7875 m/s

Therefore, the speed of your car, presuming the police was parked, is approximately 0.79 m/s.

User Bhetzie
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