Have you ever sat by a road or a railroad and listened to
the cars or trains coming by? As the car or train approaches, the whine or
pitch of the sound rises and as it recedes away from you, the pitch goes down.
This is because of something called the Doppler Effect.
The Doppler Effect works because as a wave source approaches
an observer, the wavelength of the wave decreases, which in turn increases the
frequency. As the source goes away from the observer, the wavelength increases,
decreasing the frequency.
In the above picture, the source in
this case is a star. The wavefronts are the circles surrounding the star. To
the left, the observer sees the star approaching; therefore the wavefronts are
closer together, meaning a shorter wavelength and higher frequency. The observer
on the right sees the star moving away, and they see the wavefronts getting
farther and farther apart.
For all waves, whether sound waves or light waves, the speed
of the wave is related to the frequency and the wavelength of the wave. We
relate them in this way:
v=λf
where:
- v is the velocity (or speed) of the wave
- λ (Greek letter lambda) is the wavelength of the wave
- f is the frequency of the wave (in units of 1/seconds). Sometimes, frequency is shown as ν (the Greek letter nu)
Since we know the wave is traveling the same speed, if the
wavelength is increasing (or decreasing), the frequency in turn must decrease
(or increase).
We also know that the change in the wavelength or frequency
is also related to how fast the source is moving.
where:
- f' and λ' are the frequency and wavelength measured at the observer
- f and λ are the frequency and wavelength of the source
- v is the speed of the wave
- vO is the velocity of the observer
- vS is the velocity of the source
The velocities of the observer and the source can be
positive or negative (or zero). A positive velocity means that the source (or
observer or both) are moving towards each other. A negative velocity means that
the source (or observer or both) are moving away from each other. If the
observer is stationary (vO is zero), you get:
For sources moving towards the observer, you can see the
wavelength decreases and the frequency increases. When the source is moving
away from the observer, the opposite happens. Change the source velocity to
zero for the top two equations, and you'll see something similar.
Now, what happens if the wave is visible light? The speed of
the wave becomes c and something strange happens: the wavelengths move to
opposite sides of the visible spectrum.
As the wavelength of the light decreases (source moving
towards you), the wave changes colors and the wave shifts towards the blue end
of the spectrum. This is called blue-shift. When the wavelength increases, the
wave shifts toward the red end of the spectrum. This is called red-shift.
No comments:
Post a Comment