Video: Doppler Shift

Which of the following combinations of motion of a soundwave source and a sound wave observer does not result in the observer measuring a different frequency of the sound wave to the frequency of the sound wave as measured at the source? Assume that all motion of soundwave sources and observers are at the same speed.

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Video Transcript

Which of the following combinations of motion of a sound wave source and a sound wave observer does not result in the observer measuring a different frequency of the sound wave to the frequency of the sound wave as measured at the source? Assume that all motion of sound wave sources and observers are at the same speed.

Okay, before we get to these combinations, let’s consider what’s taking place with these sound waves. In each answer option, we’ll have a sound wave source. And the sources, we can imagine, continuously emit sound waves. These waves are sinusoidal disturbances of the material around the source. And if we pick points along this wave, one wavelength apart, say we pick points like these along the peaks. Then those peaks can be represented by what are called wavefronts, these concentric circles we’ve drawn coming from our sound wave source. We know, too, that these wavefronts aren’t stationary, but they move out from the source at the speed of sound.

Along with our source and the sound waves from it, we have an observer of these sound waves. As the sound waves from the source reach the observer, the observer perceives some frequency. This frequency is equal to the number of wavefronts that pass by the observer every second. Now, the way that we’ve drawn things, our sound wave source and our sound wave observer are stationary relative to one another. This means that the frequency of the sound waves from the source and the frequency measured by the observer are the same. If they weren’t the same, if there was a shift in frequency, from the frequency given off by the source to that measured by the observer, then that shift is called a Doppler shift. And it would be caused by any relative motion between source and observer.

Our question asks for a combination of motion of our source and our observer that does not result in a frequency shift. So as we look at various motion combinations on the following screen, we’ll look for a case where the observer and the source are stationary relative to one another. Keeping in mind that all the motion of the sources and observers, we’ll name, are at the same speed, let’s look now at those combinations.

(A) A sound wave source moves in the same direction as a moving observer. (B) A sound wave source moves toward a stationary observer. (C) An observer moves toward a stationary sound wave source. (D) A sound wave source moves toward an observer moving in the opposite direction to the sound wave source. (E) A sound wave source moves away from an observer moving in the opposite direction to the sound wave source.

All right, as we consider these five answer options, we’re looking for an option that describes no relative motion between the sound wave source and the observer of those sound waves. It’s that relative arrangement of source and observer which would lead to no frequency shift of the sound waves perceived by the observer. Starting with the scenario described in option (A), here we have a sound wave source that’s in motion in the same direction as a moving observer.

So if this dot on the left is our source and this dot on the right is our observer, then option (A) tells us that this source is in motion in the same direction as our observer. We were told earlier that all motion of sources and observers in these descriptions is at the same speed. That means that in this scenario, our source and observer move in the same direction at the same speed. In other words, the distance between these two points doesn’t change over time. Because that distance between these points is constant, there will be no frequency shift noticed by the observer. The observed frequency of the sound waves will be the same as the frequency with which they’re emitted by the source. So option (A) is an example where there is no frequency shift to the observed sound waves.

Let’s consider option (B). Here, a sound wave source moves toward a stationary observer. So if this dot on the left is our source and the dot on the right is our observer, then our source is moving toward our observer like this. That means the distance between our source and our observer is changing over time. And therefore, the measured frequency by the observer will be shifted from that emitted by the source. Because there’s relative motion between source and observer in this description, we’ll cross off this option.

Now let’s move on to option (C), where an observer moves toward a stationary sound wave source. If, once again, our source is on the left and our observer is on the right, here, our source is stationary while our observer moves toward it. Under these conditions, the distance between our source and observer will change over time. And therefore, our observer will measure a frequency shift compared to the frequency given off by the source. The relative motion between the two means we’ll eliminate option (C) as well.

Now let’s look at option (D), where a sound wave source moves toward an observer moving in the opposite direction to the sound wave source. In this situation then, our source and our observer move toward one another. Therefore, the distance between them does change over time. And so there will be a measured frequency shift by the observer. We eliminate option (D).

And lastly, considering option (E), here a sound wave source moves away from an observer moving in the opposite direction to the sound wave source. Here, rather than moving toward each other, our source and observer move away from one another. Once more, the distance between them changes in time. And therefore, the observer will measure a frequency shift. This lets us cross off option (E) as an answer choice.

So it’s option (A) which shows us a combination of movement that leads to no frequency shift between the observer and the source. This happens when the sound wave source moves in the same direction at the same speed as a moving observer.

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