Video Transcript
Which of the following statements is a correct description of the Doppler shift? (A) The Doppler shift is the motion of a source of sound waves due to the reaction force produced by the waves when they are emitted. (B) The Doppler shift is the apparent change in the direction of waves depending on how the source of the waves moves compared to an observer of the waves. (C) The Doppler shift is the apparent change in the amplitude of waves depending on how the source of the waves moves compared to an observer of the waves. And lastly option (D), which will show up here at the top of the screen, the Doppler shift is the apparent change in the frequency of waves depending on how the source of the waves moves compared to an observer of the waves.
Alright, so we want to identify which of these four descriptions is an accurate definition of the Doppler shift. Each option talks about a source of sound waves. We could say that that source is this dot here. And we can model the sound waves the source emits using these wave fronts, concentric circles coming from the source. The Doppler shift has to do with how these wave fronts are perceived by an observer outside of the source. Specifically, it refers to the relative motion, if any, between the source of the sound waves and the observer.
If we consider our answer options describing this shift, option (A) speaks of a motion of a source of sound waves due to a reaction force produced by the waves when they are emitted. The trouble with this description though is that when these sound waves are emitted from our source, they don’t exert a force on the source. If they did, we would expect a sound wave source that emitted waves only in one direction, like this here, to be pushed away from those sound waves by this so-called reaction force. But that’s not what takes place. And the reason is that these sound waves don’t produce a reaction force on the source they’re emitted from. So option (A) isn’t a physically correct explanation of what goes on when sound waves are emitted from a source. And it’s not a definition of the Doppler shift.
That leaves us with options (B), (C), and (D). Looking at these three options, we see that they’re identical except for one thing. All of them speak to the apparent change in some property of the waves given off by the source as that source moves relative to an observer of the waves. Option (B) describes the change in the direction of the waves. Option (C) talks about the apparent change in the amplitude of the waves. And option (D) describes the apparent change in the frequency of the waves. So our answer choice will come down to deciding between wave direction, amplitude, and frequency as characteristic of a Doppler shift.
To see which of these three options we should choose, let’s consider again a source of waves and an observer of those waves. Let’s say that these two dots represent those two objects. The dot on the left is our source, and that on the right is our observer. As we’ve seen, one way to show the sound waves given off by our source is to depict them as wave fronts. We do this by picking and then plotting points along a sound wave that are separated by a distance of one wavelength. Often, the points we choose to display are the peaks of a wave. That would mean that each one of these concentric circles represents the peak of a sound wave moving out in all directions from the source.
But another way we can represent these sound waves is simply using a wave diagram, like we have to the right. If we do that, then the sound wave produced by our source up here might look like this as it approaches our observer. And now we can do a bit of a thought experiment. Each one of our remaining answer options describes a property that apparently changes when there’s motion between the sound wave source and the observer of the sound waves. So let’s put our observer in motion relative to our source, which we’ll call stationary, and we’ll see what that might change about the apparent properties of the sound wave.
If our observer was put in motion, say in this direction, then we can see that that would have no effect on, for example, the amplitude of the sound wave reaching it from the source. The amplitude of a wave is a fixed property. It doesn’t depend on how that wave is observed. This tells us that option (C), which describes the Doppler shift as the apparent change in the amplitude of waves depending on how the waves’ source and the observer of the waves move relative to one another, can’t be correct because there is no apparent change in wave amplitude under these conditions. Regardless of the motion of our observer, the perceived or the apparent wave amplitude of the sound wave stays the same.
Now, let’s consider option (B), which talks about an apparent change in wave direction. Again, letting our observer move relative to this incoming sound wave, we can see that that motion doesn’t have an effect on the direction of the sound wave as it travels from the source. Regardless of how the observer moves, the sound wave direction will stay the same. It’s a fixed property of the wave. So then, the Doppler shift can’t be the apparent change in the direction of waves because that direction doesn’t change even as our observer moves relative to our source.
This leaves us with option (D), which describes the Doppler shift as an apparent change in the frequency of waves depending on this relative motion. To see whether this definition is correct, let’s go back to our model of sound waves using wave fronts, down here at the bottom of our screen. We know that these sound waves given off by our source are in motion. They move outward from the source in all directions. Eventually then, they reach the observer, and the observer perceives a particular sound frequency. This perceived frequency is based on the number of wave fronts that pass by the observer in every second of time. The more wave fronts pass by the observer in one second, the higher the measured frequency.
Now, let’s imagine putting our observer in motion relative to the source. Say that our observer is moving more or less away from the source. This motion will have an effect on the number of wave fronts that pass by the observer as the observer moves. When the observer moves away from the source like this, that number of wave fronts will decrease, leading to an apparent decrease in the frequency of the sound waves. On the other hand, if the observer moved toward the sound source, then more wave fronts per unit time would pass over the observer, leading to an apparent increase in the sound frequency.
It’s important to realize that all these apparent changes in the sound frequency, whether an increase or a decrease, are changes in the frequency perceived by the observer. They’re not changes in the actual frequency of the sound waves emitted by the source. But anyway, we do see that motion between the source and the observer affects the apparent frequency of the sound waves. And therefore we’ll choose option (D) as our answer. The Doppler shift is the apparent change in the frequency of waves depending on how the source of the waves moves compared to an observer of the waves.
