00:02
Okay, so this is a question involving a doppler shift.
00:09
And what we have here is a couple of ventricles.
00:18
So if you think about the heart, you know, here we could actually draw our heart in red, right? so like here's like a heart sort of.
00:32
And if you think about the ventricles, if you remember, it doesn't really matter, but event the heart sort of divided into four chambers like this.
00:40
And this would be our left ventricle, and this would be our right ventricle.
00:46
And it says that there's a wave that's going into it, and then it's sort of bouncing off each of these ventricles.
00:56
So it says that there's like a transducer.
01:02
And here, i'll draw the transducer over on.
01:05
On this side for reasons that'll maybe hopefully become clear in a middle.
01:09
Although it really doesn't matter, but let's say here's our transducer.
01:14
This is something that can create and receive waves.
01:18
And there's like some skin, you know, or tissue between around the whole heart or whatever.
01:28
The whole idea is this transducer, it creates a wave.
01:35
And that wave, and that wave, hits this ventricle and then it bounces off and comes back and it also you know goes all the way to the other ventricle and then it hits in it and it bounces back as well okay and and we want to figure out the speed of each of these ventricles okay and it tells us some information the information it tells us is that the speed of sound in this tissue, so that we'll call this, i'm just going to call it v, the speed of, this is the speed of sound, that's 1 ,500 meters per second.
02:27
And it tells us that the frequency, which i'm going to call it f -0, the frequency that is created by the transducer is 5.
02:38
5 .000 times 10 to the 6th hertz or we could just say that 5 .000 megahertz.
02:57
And then it tells us that the frequency that we get reflected back to the transducer from the left ventricle is a little bit less 4 .998 megahertz or 10 to the 6 and the frequency from the right ventricle is 5 .003 i think.
03:38
Yes, 5 .003 megahertz.
03:47
And it's asking us to find what the speed from the left is and the speed from the right is.
03:57
Okay.
03:59
So if you remember, there is an equation that discusses the relationship between the speeds of detectors and sources and relates those to the frequencies that of a source and the frequency received.
04:19
And that equation sort of looks like this.
04:22
F prime equals f times v plus or minus vd over v minus or plus vs.
04:45
V minus or plus vs.
04:48
And d stands for detector and s stands for source.
04:55
Source and this unsubscripted v, that's the speed of sound in the material.
05:03
And f is the original frequency, and f prime is the doppler shifted frequency.
05:13
Now, an important thing to remember here is detector and source.
05:16
Detector doesn't have to be an electronic detector.
05:20
The detector is maybe just the receiver, whatever is the receiver, seever of that wave is and s the source is whatever created that that wave that disturbance so the thing we have to be careful for i have to understand here is that there are two doppler shifts um both from the right and from the left so the transducer sends out a signal that signal is then then hits the right or the left ventricle.
06:00
And when it hits the right or the left ventricle, it is doppler shifted.
06:05
At that point, the ventricle is the detector and the transducer is the source.
06:13
Then the wave gets reflected from the ventricle and it goes back to the transducer.
06:23
So when that happens, the ventricles are the source and the detector is the and the transducer is the detector.
06:36
So we have to be careful about those things.
06:41
And so i have to sort of break it down and that.
06:43
There are sort of two doppler shifts that happen.
06:46
Okay.
06:47
So i'm going to do each one in like a different color here.
06:52
So the first i'm going to do i'm going to do the, do the left first.
07:02
Oh, and the reason i put these on, there's one other thing you have to keep in mind here.
07:06
One other thing you have to keep in mind here is which sign, sign do we choose? do we choose the positive or the negative sign? well, you have to remember that when two objects are approaching each other, the doppler shift increases the frequency.
07:26
You're going to encounter wave crests more frequently as things approach.
07:31
And you're going to encounter them less frequently as they recede from each other.
07:37
So if you sort of think about the heart, if the heart is kind of beating, right? if it was sort of, if it was going through a beat like this, okay, then what would happen here? it's like during this beat here, the right side of the heart would be moving towards the transducer and the left side would be moving away from the transducer and if we look at the the left side here we see that the left side reflects a slightly lower frequency because it moved away okay and the right side reflected a slightly higher frequency because it was moving towards okay and that's going to be important now okay so let's look at the left side first no reason to i'm just going to make that choice.
08:34
Okay.
08:36
So i'm going to say f prime from the left, that's going to equal the original frequency times v.
08:47
And then the question is, do we pick plus or minus the detector? so in this case, the detector for this first shift, the detector, is the ventricle.
08:57
And the left ventricle is moving away.
09:00
And we know that when it moves away, it drops the frequency.
09:03
So that's going to, and this is the numerator.
09:07
So on the top, to get a lower value, a lower frequency, it's going to be the minus sign.
09:12
Minus vl, that's the detector, over.
09:19
Now, this is the velocity of the source.
09:21
The source is the transducer.
09:23
The transducer is not moving.
09:25
So it's just v, because v, s is stated.
09:29
The transducer doesn't move.
09:35
So that would be it.
09:36
So now, so that was the doppler shift coming into the left ventricle.
09:41
Now what we need is the doppler shift of the reflected wave.
09:46
Now it's coming out of the ventricle and going back to the transducer.
09:51
So what we now need is i'm going to say fl and i'm going to call it double prime.
10:00
Okay, well that's going to equal this frequency, which i'm going to say that's f, that's f, that's f.
10:05
L prime and we'll sub in for that in a minute times v.
10:17
And now we're talking about the detector.
10:20
Now the detector, the detector is the transducer in this case.
10:27
And the transducer is stationary.
10:29
So it's just v over v.
10:35
And the source now is the ventricle.
10:37
But now we're in the denominator.
10:39
Okay, so what's going to reduce the frequency in the denominator? that's going to be having a bigger denominator.
10:49
So that's going to be plus vl.
10:56
Okay.
10:56
And now, fl prime, well, we know that right from here...