Before further studying the Doppler effect, let's learn the basic knowledge about waves:
If we throw a small stone into the calm water, ripples will appear on the water and continue to spread forward. At this time, whenever the water surface at the wave source vibrates, a new wave train will be generated on the water surface.
Let the vibration period of the wave source be t, that is, every time the wave source vibrates t times, the distance between two adjacent wave trains on the water surface is VT, where v is the propagation speed of the wave in the water. In physics, we call the distance between the wavelengths of such adjacent wave trains, which is represented by the symbol λ. In this way, the relationship among wave wavelength, wave velocity and vibration period can be expressed as λ=VT (1).
Because it takes t for a wave source to vibrate once, the number of times the wave source vibrates per unit time is 1/t. In physics, the number of times the wave source vibrates per unit time is called the frequency of the wave, which is expressed by f, so its relationship with the period can be expressed as f= 1/T, or T= 1/f (2).
Combining (1) and (2), we can get λ=VT=V/f (3).
This formula is the basic formula for us to discuss problems related to waves. Although it is summarized from the propagation of water waves, it is applicable to all waves.
Experimental research shows that the wave propagation velocity V is a constant for a given medium. Therefore, when a wave propagates in a medium, its wavelength λ is directly proportional to its period (inversely proportional to its frequency). That is, the higher the frequency of the wave, the smaller the period and the shorter the wavelength; Conversely, the lower the frequency, the longer the period and the longer the wavelength of the wave.
For sound waves, the frequency of the sound determines the tone of the sound. That is, the higher the frequency of sound waves, the higher the tone of sound waves, the sharper, thinner and even harsher the sound. According to the above conclusions, the sound source that produces treble vibrates slowly, the vibration period is longer, and the wavelength of the corresponding sound wave is longer. For example, the wavelength of 10000Hz sound wave is1100 of the wavelength of 100Hz sound wave.
In visible light, the frequency of light waves determines the color of colored light. The frequencies from low to high correspond to red, orange, yellow, green, blue, indigo and purple. Red light has the lowest frequency and the longest wavelength. Purple light has the highest frequency but the shortest wavelength.
Let's discuss the Doppler effect of light with the above background knowledge:
Suppose a light source emits a wave train every t, that is, the period of the light source is t, as shown in the figure, when it is stationary, the time interval between two adjacent wave trains is t and the distance interval is λ=cT.
Where c stands for the speed of light.
When the light source leaves the observer at the speed v, the distance that the light source moves in the time between every two adjacent wave trains is VT, so the time required for the next peak to reach the observer increases by VT/c, so the time required for two adjacent peaks to reach the observer is:
T ' = T+VT/c & gt； T
That is, compared with the observer, the period of light wave becomes longer and the frequency becomes lower. According to the relationship between the above frequency and light color, the color of secondary light will shift to red light. In physics, this phenomenon is called redshift.
At this time, the distance between two adjacent wave trains to the observer, that is, the wavelength, becomes λ'=cT+VT.
That is, the wavelength becomes longer. The ratio of these two wavelengths is λ'/λ = t'/t =1+v/c.
That is to say, the wavelength increases by V/C. We call this relative increase red shift, which depends on the distance speed of the light source. Because in general, v
For example, the Virgo galaxy cluster is leaving our galaxy at a speed of about 1000 km/s, so the wavelength of any spectral line in its spectrum is larger than the normal value by a ratio λ'/λ =1+v/c =10000/300000 =
If the light source moves towards the observer, just change V in the above formula to-V. The difference is that there will be a blue shift of light at this time.
According to the moving speed of the light source, we can calculate the offset of light in the spectrum; On the contrary, according to the shift of light in the spectrum, we can also calculate the moving speed of light source relative to us. Knowing this, it is not difficult for us to understand the discovery process of Hubble's law.
Point wave source in motion: Doppler effect and seismic wave
We have all had the experience that when a police car or ambulance approaches from a distance, it seems that its alarm frequency is getting higher and higher.
And it's getting farther and lower.
Christian Andreas Doppler first explained this effect:
When the sound source approaches the observer, the front wave is compressed due to the motion of the sound source, so the perceived frequency increases.
On the contrary, when you are far away, the distance between wave fronts increases and the induction frequency decreases! As shown below: the wave source moves to the right.
The frequency change of listening is continuous, but why does the textbook mention the formula value of frequency change?
But it's fixed? What are the restrictions?
For the light source, there is a similar phenomenon, as shown below: the wave source moves to the left.
Observers in different directions will see blue shift and red shift respectively.
For example, by observing that the spectra of all planets in the universe have a red shift phenomenon, that is, all planets seem to be far away from us.
Inferring that the universe is still expanding.
The following Java animation allows you to see the Doppler effect felt by a stationary observer at various wave source speeds.
variable parameter
The wavelength of the wave velocity and the propagation speed of the wave source (hold down the top of the corresponding arrow with the mouse and drag the mouse)
If you press the mouse button in the window, you will pause the animation and press it again to continue.
When the traveling speed of the wave source is greater than the wave speed, a shock wave will be generated.
Physical explanation:
As shown in the figure below, when the insects on the water swing their limbs in situ, they will produce water waves that scatter around.
If a bug swims forward by swinging its limbs, we may observe the water waves below.
(When the worm's swimming speed is less than the water wave's propagation speed)
If the wave velocity is exactly equal to the moving speed of the wave source, the following figure will be produced.
The following figure synthesizes the situation at different speeds, where V is the speed of insect swimming and vw is the wave speed of water wave.
In fact, the above situation applies to all fluctuations, water waves and sound waves.
When the moving speed of the wave source is greater than the speed of the wave itself, a triangular (three-dimensional: conical) wavefront will be formed.
All the waves arrive at the front at the same time, so the waves are superimposed to form a shock wave.
The picture below shows the cone-shaped area of shock wave formed by supersonic aircraft flying.
Supersonic aircraft will produce two shock waves, as shown in the left picture below.
Because the plane flies faster than sound, A has seen the plane in the picture on the upper right.
But I haven't heard the shock wave generated by the plane (just arrived in B).