17. The Doppler Effect.

If either the source or the receiver of a wave are in motion the apparent wavelength and frequency of the received wave change. This is apparent shift in frequency of a moving source or observer is called the Doppler Effect. The speed of the wave is not affected by the motion of the source or receiver. This simulation looks at the Doppler effect for sound; the black circle is the source and the red circle is the receiver. Time is in hundredths of a second and distance measured with the mouse is in meters. A similar effect occurs for light but in that case the source and receiver cannot travel faster than the wave speed (the speed of light).


Note: Animations may take a few seconds to load.

 

Questions:

17.1. Click the following button and then click 'play' to see a stationary source and receiver. Verify that the period at the receiver (time elapsed from when one wave reaches the receiver until the next one reaches it) is 0.005 s (note that in the simulation a "1" corresponds to 0.01 s). What frequency does this sound wave correspond to?

17.2. After there are several waves in the simulation pause it and use the mouse to find the wavelength (distance between two successive crests). What is the speed of the wave (wavelength/period)?

17.3. Now look at the following case where the receiver is moving. Use the step button above to find the period (time between crests) as measured by the moving receiver when it is on the right of the source (moving towards the source). What is the frequency at the receiver if it is moving towards the source?

17.4. When the receiver gets to the left of the source (moving away from the source) pause the simulation and measure the period. What is the frequency at the receiver if it is moving away from the source?

17.5. The following button will show the source moving but the receiver stationary. Again find the frequency while the source is on the left, moving towards the receiver and the frequency when it is on the right moving away.

17.6. The following button shows a source moving faster than the speed of the sound wave. In this case all of the wave crests arrive together forming a shock wave or "sonic boom". Why can this not happen in the case of light from a moving light source?

Although these simulations have not shown this, both the effects of a moving source and a moving observer can happen at the same time. The equation for the Doppler shift with both a moving source and observer is given by  where f' is the received frequency, f is the original frequency, v is the speed of the wave, vO is the speed of the observer and vS is the speed of the source. The upper signs in the equation are used if either the observer or source is moving towards each other and the lower signs are used if the either object is moving away from the other (so if the observer is moving towards the source but the source is moving away from the observer the equation to use is ).

17.7. For the case of the moving receiver and stationary source (vS = 0) use the original frequency you found in question 17.1, the shifted frequency (f') you found in question 17.3 and the speed of sound you found in 17.2 to find the speed of the observer.

Electromagnetic waves will also undergo a Doppler shift except that the relative velocity between the source and observer can never be larger than the speed of light and the formula for calculating the shift is slightly different. For electromagnetic waves we have where v is the relative speed between the observer and source (positive if they are approaching and negative if they are moving away from each other) and c is the speed of light.

17.8. As you can see from question 17.7, if the speed of the wave is known and the original and received frequencies are know the speed of the source or observer can be found. Explain how you could determine the speed of a car or thunderstorm by bouncing radio or microwaves off of them.

17.9. If a car goes past with its radio blaring we easily hear the Doppler shift for sound as the car passes (the sound appears to shift from a pitch which is too high to one which is too low). But if a car goes past with its lights on we do not notice the Doppler shift for light (the color does not seem to shift towards the red frequencies). Explain why this is so. (Hint: Try plugging in some numbers for a car speed in the equation for the Doppler shift for light).

17.10. If an astronomer notices that the spectrum of colors coming from a star are all shifted towards the red end of the spectrum (the frequencies are lower than they should be) what can she conclude about the motion of the star relative to the earth?
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