Kaplan Doppler Question

[SSerenity]

I don't understand their reason for using the doppler equation in the form that they did. In this case, the sound SOURCE and the sound DETECTOR are the same, so I believe we need to use a different equation.

In Khan Academy's video, they derive a different equation for when the source & the detector are the same, such as in this example. The formula they arrive at is in the green box



can someone explain when I'm supposed to use Khan's equation or not?

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[theonlytycrane]

We shoot sound waves from the device at the vena cava. When they bounce back to the device, the vena cava becomes the source and the device becomes the detector.

Stick with just the one equation and forget the Khan stuff:

where "d" stands for detector and "s" stands for source. v is the speed of sound in the medium and you choose the sign based on remembering that "top is toward".

In this case vd = 0 and we choose the + sign on the bottom because the blood is going away from the detector.

 

[SSerenity]

If the blood was the original source of the sound, then we would have just one shift, and I agree that equation above makes sense.

But in this case, the blood perceives the sound at a changed frequency. Then it becomes the "source" and reflects that shifted sound while it moves. Hence a second shift. So there are two shifts in this case, which is what khan was trying to explain.

Why would we ignore the second shift in this example?

 

[theonlytycrane]

A shift in either case is perceived- no actual change in frequency of the sound wave is occurring. If both source and detector are stationary, the frequency of the sound sound out is what we detect back in return.

The blood acting as the initial detector will perceive a different frequency than the device acting as the detector later on. But these perceived frequencies don't affect one another because the true frequency is constant.

We're not ignoring the second shift, it's just that the perceived frequencies are specific only to each detector (we wouldn't combine them).

 

[wizzed101]

I believe the Khan explanation is the correct one.
In this case it should be 10^7 * (1499.6)/(1500.4)

HOWEVER, the take home message here is that the reflected sound's frequency must be LESS than the original sound wave that leaves the detector because blood is moving AWAY from the detector. In a real test, even if there was a mistake, you should have just chosen C and moved on (B used wrong unit).

This is a fun question that is very MCAT like imo, but not for the reason Kaplan thinks lol