This is known as relative motion, the speed of objects depends on the frame from which they are measured. If on the contrary you were moving in the same direction as the train, the train would appear to move slower, or even stationary if your speed is identical to that of the train. In the following equation, the Doppler shift (denoted by the letter z z) is calculated by comparing (i.e., taking the ratio of) the difference ( ) between the observed wavelength ( obs o b s) and the rest wavelength ( ). By the end of this section, you will be able to: Explain why the spectral lines of photons we observe from an object will change as a result of the object’s motion toward or away from us. The train also appears to be moving faster than it does when you are stationary. Of course, the train itself is moving at a constant speed, but according to the observer the train is moving faster. This reference wavelength is called the rest wavelength. ![]() But the frequency with which you are seeing each new car as you are moving in the opposite direction of the train is greater than if you were stationary. The distance between the cars of the train appears the same to you, so the wavelength is the same. The observer is you in the moving vehicle, and the train represents the moving wave. ![]() Let us think of this in terms of an analogy. Imagine you are driving in a vehicle with a train on tracks parallel to the road approaching you. But how is this possible if the wavelength remains the same and the medium does not change? Thus, the frequency according to the observe increases. If the blue dot representing the observer moves toward the source in Figure 8.4.1, it would flash more frequently since it would encounter crests more often, than it would if stationary. A moving observer would measure the same distance between crests as it would if it was stationary. So, they have a velocity relative to this medium v. Relative to us, we observe such a change if an emitter of a wave is moving relative to us. Thus, in this scenario the wavelength is fixed. The Doppler effect is a change in the frequency of a wave which occurs if one is in a different frame of reference from the emitter of the wave. In this case since the source is stationary the distance between the crests is the same in front and behind the source, as shown in the animation of Figure 8.4.1. Let us consider what happens when, instead of the source, the observer is moving toward or away from a stationary source. ![]() Where the sign is a plus for a source moving away from the observer and a minus for a source moving toward the observer.
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